The Rohirrim, why horses?

[Morthoron]

Originally Posted by Lastande Took

A soldier on horseback has a huge advantage over a soldier fighting on foot.

Amusingly, that was not always the case in Middle-earth (and certainly not the case for the flower of French chivalry at Crecy and Poitiers). For instance, the Numenorean infantry was the most formidable force of the 2nd Age. Sauron's legions folded up their tents and headed for the mountains at the very sight of them.