When it comes to the Indian Wars, it is the cavalry that gets the glory and screen-time. In reality, the infantry or “walk-a-heaps” (as Sioux are reported to have called them) played a significant role. Prolonged travel tires horses. Over a period of weeks seasoned infantry can outdistance cavalry or other horse-mounted raiders.
It seems some of the lessons learnt during the War between States were retained. I came across this interesting passage in the Osprey book “Men-at-Arms 063: The American Indian Wars 1860-1890”
An 18th Infantry captain, Anson Mills, at Fort Bridger in 1866 had his post saddler make leather looped belts for his men, personally obtaining a patent on the idea. In late 1876 the Ordnance Department, which had consistently preferred boxes to belts, finally gave in to popular pressure and had 30,000 canvas and leather 'prairie' cartridge belts made at Watervliet Arsenal. By then virtually no cartridge boxes had been used out West for a number of years.
This light-weight belt had another advantage, besides bringing in a fair sum of royalties to Captain Mills. It reduced the fighting man's load. The Indian-fighting infantryman became one of the lightest loaded soldiers in the world. Lieutenant W B. Weir in 1877 listed an infantryman's full field equipment load as:
60 rounds ammunition and belt 5.40 lbs
overcoat 5.25 lbs
blanket (grey wool) 5.13 lbs
rubber blanket (ground cloth) 3.00 lbs
Springfield rifle and sling (bayonet ommitted [sic] from this list) 8.40 lbs
extra clothes 2.00 lbs
full canteen (one quart) 3.84 lbs
five rations: 3/4 lbs meat and 1 lb hardtack per day 8.75 lbs
Total 41.77 lbs (18.79 kg)
Officers, who generally carried a pistol and often some sort of rifle, carried about the same weight. Sometimes the men went even lighter, as shown in General Field Orders No. 2. Department of Dakota, 10 August 1876, in an anti-Sioux campaign: 'No tents whatever will be carried, no companv property, no cooking utensils except tin cups, no. bedding (except one blanket per man) … 100 rounds of ammunition (per man) …Everv infantry officer and man will carry with him two days' cooked rations.'
Osprey “Men-at-Arms 438: US Infantry in the Indian Wars 1865-91” notes: “Most infantrymen on campaign preferred to leave their packs behind at barracks, and carried personal items rolled in blankets slung around their bodies. When the 5th Infantry were ordered on campaign in July 1876. each soldier took only a blanket, a shelter-half, an extra pair of shoes and one change of underwear, plus weapons and ammunition. Sibley tents, iron stoves and other unit gear were carried in company wagons; more lightly equipped columns used pack mules.”
No information on how many wagons a company had is given, but “Hardtack and Coffee” informs us that each ACW Union Infantry company would have two wagons and five for the Regimental HQ.
Men at Arms 438 provides the information that companies were small units compared to modern versions:

Each of the post-July 1866 regiments of infantry was to be composed of one colonel, one lieutenant-colonel, one major, one adjutant and one regimental quartermaster (both of the latter being extra first or second lieutenants), one sergeant-major, one quartermaster sergeant, one commissary sergeant, one hospital steward, two principal musicians, and ten companies. Each infantry company consisted of one captain, one first lieutenant, one second lieutenant, one first sergeant, one quartermaster sergeant, four sergeants, eight corporals, two artificers, two musicians, one wagoner and 50 privates. The number of privates in a company could be increased to 100 when needed.

Note that only one wagoner is listed.

Later on in this section it is stated the average size of a company would be 35 men.

The company was the key operational unit. If a company was relatively small, the platoon level was omitted.

A platoon had two sections, each of two or more squads. Typically a squad would be a corporal and seven privates.

Interestingly, military reformer Emory Upton proposed soldiers manoeuvre and skirmish in units of four, so squads might be further divided.