[Legbreaker]

I tend to think that while true Cavalry units will have horses, there will be more manpower mounted on bicycles. Bikes are far easier to train for, require less upkeep, don't run away in the face of danger, etc.
Bicycles would probably be in great demand for otherwise foot mobile infantry - bicycles are the most efficient form of transport (require less energy input for great gain). The bicycles may not be an officially issued item though, and would probably be left behind with the HQ/supporting units when contact with the enemy was expected.

Horses definitely have their advantages with load carrying and movement over rough terrain, however they have many drawbacks also. There is a place for them in the military, but I don't see that place as in the fighting itself, but rather as a form of transport for soldiers who dismount short of the engagement area and move the last short distance to fight on foot.

It seems very unlikely though that military units would see much need for horses prior to fuel and parts reserves being expended (or close to them) and supply lines reduced to a dribble. A truck is far superior for transportation of supplies or troops than a team of horses.

With the lack of horse skills in the modern world, I can't really see horses being used informally early on. In other words, while all the vehicles may be stripped from a stationary artillery unit, it's extremely unlikely anyone in the unit would have the skills to use horses to shift the guns about the firebase - manpower would be used almost exclusively.