Both players and horses get xp.
Players get XP by:

• Entering shows
    For each show entered, a Manufacturer gets 10 XP, an Equilibrium 12 XP, a Rider 15 XP and a Trainer 10 xp.
• Winning shows
    If your horse finishes in Top 20 in a show, your player will get some more xp. 50 XP for 1^st place, 10 XP for 20^th place.
• Manufacturing tack
    You get 50 XP for creating or repairing tack and intermediary items.
• Working as a stablehand
    You get 40 XP for each horse that you feed. The xp will go up the more you work.
• Working as a vet
    You get 50 XP for each scheduled horse that you treat and 25 XP for market horses.The xp will go up the more you work.

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Horses get XP by participating in shows.
They get 10 XP for each show they've entered. On top of that, they get 10 to 50 XP more, if they finished that show in Top 20.
Riders can also add XP to their horses, using their skill. The amount of XP depends on the skill %.

**Players in the Trainer and Rider guild also gain 1000 XPS every so often when they are working in their arenas or barns.