What are the repercussions?
Reindeer and cammels can also be ridden but are a bit specialised to there climates and not very suitable for battle. Oxen can be outrun by man. No predator is suitable for ridding and would be completely unecconomical STOP THOSE THOUGHTS!
This is infantry wank. If you dont take any animals with you an army can actually march further in a day horses provide tactical mobility at the expence of strategic mobility.