I am fortunate in the sense that most of my horses tend to need to the same routine. There's little adjustments as we go of course, but for the most part it's the same.
I really like to start with a big, long, elastic trot. Dressage-pony-is-us.
Big strong posting trot for several laps, bumping them up into the bridle, softening to the bit and really asking for them to reach out and engage that hind end. Once I feel they get most of that initial energy out and get loosened up, we walk a lap.
After that I like to do a couple laps loping, doing a lot of speed transitions. Start off slow, loose, relaxed. I like to warm up kind of in a reiner position, especially on Selena who actually was a finished reiner before I got ahold of her. I'll do it in incriments. Bump-bump, little faster, give my rate command and slower again. Bump-bump, faster again, this time pushing a little more, then give my rate command and bring them back. Each time I push the speed a little faster and a little faster, just seeing if they are going to push on me and remind them about their rate. If I draw later and get to have a less crowded warmup, I like to really push on the long side of the arena and just let them fly then soften them more to the rate on the short end by sitting and just lightly bringing them back. I rarely get to really speed up but on occasion I'll get to a race and be able to.
After we've done that, I like to go reinforce my turns a little. Find some fence space, do two or three rollbacks into the fence. Both of these let me know I have my run, rate, and turn down.
To end the warmup I go to the middle of the arena and do some haunch/forehand turns, sidepassing, counter arc circles, essentially kind of a "cool down" moment while still making sure we're loosened up and ready to go.