I would reckon that as soon as the war goes nuclear, armies are going to start confiscating horses as a matter of course when near to or passing through a horse-friendly area. In many cases, I think that they would beat the desperate hordes of civilian carnivores to the punch. Horse usually ends up pretty far down the list of possible meal items in disaster scenarios. Usually, horse starts showing up on the menu when folks are on the verge of starvation. Stored/preserved food usually goes first and if governments are acting responsibly (oxymoron?) to prepare for a possible, nay likely, impending nuclear war, there should be enough of that on hand to stave off starvation for at least 3-6 months. During this "grace period", militaries would be grabbing up all of the horses they can get their hands on.
As to the bicycles vs. horses debate, I think that military bikes would be common in the T2K verse, perhaps even more common than horses.
Yes, bikes can be produced by fairly simple factories, but I don't think that their manufacture would be a high priority when the armies of the late Twilight War are all clamoring for more purely military items like ammo and uniforms.
In WWII, the TOE for German Volksgrenadier divisions called for a bicycle-mobile regiment. Usually, this regiment acted as the division's operational mobile reserve.
http://forum.juhlin.com/showthread.p...volksgrenadier
The biggest edge that the horse has over the bicycle is cross-country mobility. Yes, mountain bikes are capable of some pretty amazing things when ridden by a highly experienced rider. But they can't carry the same load
and cross the same kinds of terrain that a horse can.