Yes, more distinguishable horse characteristics are needed.
Each horse can have different characteristics and conditions like:
- F-Speed
- F-Acceleration
- F-Maneuverability
- F-Trample
- F-Armor
- F-Capacity
- B-Lame
- P-Perks
Perks are added to the horse capabilities or the rider, and should not be anything overpowered.
Those characteristics can change in the course of the game, as you can train the horses, use horse armors, send them to professional trainers, use enchanted bridles, they can get lame and need to recover, and so on...
Just my two cents.