Have 2 or 3 extra horses in your inventory (I'm not sure if this actually make you go faster). Have more mounted units than infantry This can be expensive, but an army with many cavalry units will travel faster than an army with lots of infantry units. Increase your Pathfinding skill It will make you go faster in the map. If your Athletics skill is 4 and your Riding skill is 3, you will go faster on foot than on a horse in the map.

Increase your Athletics or Riding skills You can go faster in a horse with a high Riding skill, or faster on foot with a high Athletics skill. You can put horses on your inventory and the effect will be reducted, but don't put too many horses or can end up going even slower than before. Don't have many goods in your inventory Carrying lots of goodies will make you go slower. Disband some units Sometimes you may have some units you don't actually need (like bandits), you can put 'em on a garrison or disband them, and you may gain some speed. Make sure your army has high morale, get food or win some battles to grow it up.

Mount and blade warband speed up time