[Panther Al]

Not disagreeing- bikes will be a lot more common than horses, after all even with things being as messed up as they are, setting up a small bike factory would be relatively easy (not so sure about sourcing tyres, but...). In fact I think most infantry units will be awash in them.
My point is that the use of the unit will shape if its horse mounted or bike mounted. Bikes are limited in that if you want to carry more than yourself and 20 or so kilos of stuff you need trucks, and the stills that goes with them. But you don't need any specialised personnel and feed horses will. Horsed units on the other hand can pull wagons and artillery, can, for the most part, live off the land with little or no supply of "tech". But, they do require training, both to ride as well as trained farriers, vets, etc.
So: a few horse units yes, primarily in the scout/screen/raid type of uses, but the bulk of the average joe's in the larger units riding bikes as much as possible, just in a non-tactical way.