I love yoga, it learned me how to breath properly, and it helps me so much during jumping sessions for example.
I swim a lot! It helps with my general shape, it especially strengthens my back which is so important to ride 🙂
Cardio is really great for endurance. A lot of professional riders also do yoga, which is really good for your muscles
The most important on horse riding is the breath, and for that; no secret: running ;)
Then you can work on your legs by doing squats, running the stairs, then core exercices like obliques for a better balance, crunches and plank, flutter kicks can also be great.
Don't forget back exercices like "superman".
I hope I could help you :)