In his writings, Clausewitz identifies a number of key features of supply by horse-drawn armies, firstly that the balance of the types of units making up the army is important in determining their supply. Too much cavalry or artillery or baggage train reduces both the mobility of the army and the demand for fodder can overwhelm the supply service in various circumstances. Secondly he demonstrates that different types of supply have varying levels of administrative efficiency, while some are positively destructive, but the determining factor in which one to employ is the ability of the local area to provide the supplies. He even goes so far as to give us an estimate of the density of population required to support a Corps sized force for a few days. When Clausewitz refers to 'miles' he is using the Prussian mile of 7.5 km as his measurement, so he is referring to a population density of 35 to 55 inhabitants per km sq and the Corps needing an area of 225 km sq with sides of 15 km long.
1.—Living on the inhabitants, or on the community, which is the same thing.
"If we bear in mind that in a community consisting even as it does in great towns, of consumers only, there must always be provisions enough to last for several days, we may easily see that the most densely populated place can furnish food and quarters for a day for about as many troops as there are inhabitants, and for a less number of troops for several days without the necessity of any particular previous preparation. In towns of considerable size this gives a very satisfactory result, because it enables us to subsist a large force at one point. But in smaller towns, or even in villages, the supply would be far from sufficient; for a population of 3,000 or 4,000 in a square mile which would be large in such a space, would only suffice to feed 3,000 or 4,000 soldiers, and if the whole mass of troops is great they would have to be spread over such an extent of country at this rate as would hardly be consistent with other essential points. But in level countries, and even in small towns, the quantity of those kinds of provisions which are essential in war is generally much greater; the supply of bread which a peasant has is generally adequate to the consumption of his family for several, perhaps from eight to fourteen days; meat can be obtained daily, vegetable productions are generally forthcoming in sufficient quantity to last till the following crop. Therefore in quarters which have never been occupied there is no difficulty in subsisting troops three or four times the number of the inhabitants for several days, which again is a very satisfactory result. According to this, where the population is about 2,000 or 3,000 per square mile, and if no large town is included, a column of 30,000 would require about four square miles, which would be a length of side of two miles. Therefore for an army of 90,000, which we may reckon at about 75,000 combatants, if marching in three columns contiguous to each other, we should require to take up a front six miles in breadth in case three roads could be found within that breadth.
If several columns follow one another into these cantonments, then special measures must be adopted by the civil authorities, and in that way there can be no great difficulty in obtaining all that is required for a day or two more. Therefore if the above 90,000 are followed the day after by a like number, even these last would suffer no want; this makes up the large number of 150,000 combatants.
Forage for the horses occasions still less difficulty, as it neither requires grinding nor baking, and as there must be forage forthcoming in sufficient quantity to last the horses in the country until next harvest, therefore even where there is little stall-feeding, still there should be no want, only the deliveries of forage should certainly be demanded from the community at large, not from the inhabitants individually. Besides, it is supposed that some attention is, of course, paid to the nature of the country in making arrangements for a march, so as not to send cavalry mostly into places of commerce and manufactures, and into districts where there is no forage.
The conclusion to be drawn from this hasty glance is, therefore, that in a moderately populated country, that is, a country of from 2,000 to 3,000 souls per square mile, an army of 150,000 combatants may be subsisted by the inhabitants and community for one or two days within such a narrow space as will not interfere with its concentration for battle, that is, therefore, that such an army can be subsisted on a continuous march without magazines or other preparation."
"If circumstances are less favourable, if the population is not so great, or if it consists more of artisans than agriculturists, if the soil is bad, the country already several times overrun—then of course the results will fall short of what we have supposed. Still, we must remember that if the breadth of the front of a column is extended from two miles to three, we get a superficial extent of country more than double in size, that is, instead of four we command nine square miles, and that this is still an extent which in ordinary cases will always admit of concentration for action; we see therefore that even under unfavourable circumstances this method of subsistence will still be always compatible with a continuous march.
But if a halt of several days takes place, then great distress must ensue if preparations have not been made beforehand for such an event in other ways. Now these preparatory measures are of two kinds, and without them a considerable army even now cannot exist. The first is equipping the troops with a wagon train, by means of which bread or flour, as the most essential part of their subsistence, can be carried with them for a few, that is, for three or four days; if to this we add three or four days' rations which the soldier himself can carry, then we have provided what is most indispensable in the way of subsistence for eight days.
The second arrangement is that of a regular commissariat, which whenever there is a moment's halt gathers provisions from distant localities, so that at any moment we can pass over from the system of quartering on the inhabitants to a different system."
2.—Subsistence through exactions enforced by the troops themselves.
"The result is, therefore, that the subsistence of troops by forced contributions in this manner can only be adopted with success when the bodies of troops are not too large, not exceeding a division of 8,000 or 10,000 men, and even then it is only to be resorted to as an unavoidable evil."
3. —By regular requisitions
"In all assemblages of troops in their own country there is no difficulty in subsisting by regular requisitions; neither, as a rule, is there any in retrograde movements. On the other hand, in all movements into a country of which we are not in possession, there is very little time for such arrangements, seldom more than the one day which the advanced guard is in the habit of preceding the army. With the advanced guard the requisitions are sent to the local officials, specifying how many rations they are to have ready at such and such places. As these can only be furnished from the immediate neighbourhood, that is, within a circuit of a couple of miles round each point, the collections so made in haste will never be nearly sufficient for an army of considerable strength, and consequently, if the troops do not carry with them enough for several days, they will run short. It is therefore the duty of the commissariat to economise what is received, and only to issue to those troops who have nothing. With each succeeding day, however, the embarrassment diminishes; that is to say, if the distances from which provisions can be procured increase in proportion to the number of days, then the superficial area over which the contributions can be levied increases as the squares of the distances gained. If on the first day only four square miles have been drawn upon, on the next day we shall have sixteen, on the third, thirty-six; therefore on the second day twelve more than on the first, and on the third day twenty more than on the second."
"But now, if a war is not so decisive in its results, if its operations are not so comprehensive as is consistent with its real nature, then the requisition system will begin to exhaust the country in which it is carried on to that degree that either peace must be made, or means must be found to lighten the burden on the country, and to become independent of it for the supplies of the army. The latter was the case of the French army under Buonaparte in Spain, but the first happens much more frequently."
""Not only were stores of provisions collected, either by purchase or by deliveries in kind from the landed estates (Dominiallieferungen), consequently from distant points, and lodged in magazines, but they were also forwarded from these by means of special wagons, baked near the quarters of the troops in ovens temporarily established, and from thence again carried away at last by the troops, by means of another system of transport attached to the army itself. We take a glance at this system not merely from its being characteristic of the military arrangements of the period, but also because it is a system which can never be entirely done away; some parts of it must continually reappear."
Supply of fodder for horses
"The feeding of horses by an artificial system of supply is, however, an experiment which has not been tried, because forage is much more difficult to provide on account of its bulk. A ration for a horse weighs about ten times as much as one for a man, and the number of horses with an army is more than one-tenth the number of men, at present it is one-fourth to one-third, and formerly it was one-third to one-half, therefore the weight of the forage required is three, four, or five times as much as that of the soldier's rations required for the same period of time; on this account the shortest and most direct means were taken to meet the wants of an army in this respect, that is by foraging expeditions. Now these expeditions occasioned great inconvenience in the conduct of war in other ways, first by making it a principal object to keep the war in the enemy's country; and next because they made it impossible to remain very long in one part of the country."
"Forage, of which, as we have before said, there is usually at first the least deficiency, will run short soonest if a country begins to become exhausted, for it is the most difficult supply to procure from a distance, on account of its bulk, and the horse feels the effect of low feeding much sooner than the man. For this reason, an over-numerous cavalry and artillery may become a real burden, and an element of weakness to an army."
Clausewitz served with the Russian Army for the 1812-14 campaigns only rejoining the Prussian Army in time for the 1815 campaign. During his time in the Russian Army, the supply service did not always run smoothly and there were numerous instances of failures by the commissariat. Further reading can be found in the section "Supply System and Administration of the Army" of this Russian Army website.