Yes. Warm-up is a key to a good training!
I think it's essential to warm-up and stretching because, first of all we do that for our horses so why not for us too? And also we are fighting to say that horse riding is a sport so let's act like it's one ;) I think it's a shame that clubs don't teach it to riders, it gives them bad habits.
For the warm-up, you already do it when you groom your horse (walking to field, grooming, picking feet out warms up your lower back and helps with your balance).
It is very useful because it prepares you body to the physical effort by rising up your body's temperature, it improves your performances and avoids injuries (reduces articular friction and rises the muscles' stretch)
You can continue your warm-up on your horse at the beginning of your session with your shoulders and your back to have better precision in your actions but also your ankle, neck and pelvis.
For the stretching, it helps finding back your breath, relax the muscles and limit the risks of tendonitis or even muscle tear. The most important parts to stretch are the inside of the tights, the calf and back.
I hope i could help you :)