Okay so from the top:
Weapons: lasted literally centuries and were carried on the backs of the men. The logistical burden of weaponry is identical in home territory or overseas.
Ammunition: this is an era of cast lead shot (in the early eras you had stone shot, arrows, and bolts). All of this was reusable. As long as you won, you go find the spent shots, heat up a crucible, and pour the lead into a mold (which could be little more than a hole in sand). The logistical burden of ammunition was virtually identical in home territory or overseas. You could march a little bit faster if you could rely of magazine stored munitions, but this was a convenience, not a necessity.
Powder: This had a real logistical burden - but only if you fought. Armies (and navies for that matter) did not do so much in the way of live fire training. Yes it was hard to replace powder once expanded at the far side of the world ... but that is why everyone freaking set up powder mills in the early Caribbean colonies.
Clothing: could be looted from the peasants, everywhere
Food: could be looted from the peasants, everywhere
Water: only an issue for extreme length voyages (e.g. crossing the Pacific) or in desert terrain. Even in the later, you normally could get enough to get buy without too much trouble.
Pay: could be looted from the peasants, everywhere (most armies of the era were not paid wages and instead signed on for the privilege of looting peasants).
As long as you were fighting on land with lots of peasants that hadn't been pillaged recently, infantry were arguably cheaper to maintain in the New World than the old (at least that is what the actual surviving records indicate). In every single war, it was always cheaper to fight on someone else's land than on your own (peasants being easier to pillage then).