Was he like this in his two's also?
Do consider, he's only three, and still maturing.
It could have to do with the saddle, or it could just be an awkward baby body, figuring out bigger workouts.
Is he stalled or turned out? If he's stalled and doesn't move very much the rest of the day he's not ridden, it's understandable for him to need a bigger warm up.
It's winter. His body is out in colder temperatures. Is he like this year round?
My 14yo show horse always takes a very long warm up in the winter. Even on full turnout, where he's moving constantly, he's just simply not as ready to go and work in the winter. The summer time, I can jump right on, and he's supple from the start, and moving out very softly.
In the winter, it's a good 20-30 minutes of warming up and stretching, just so we can spend another ten minutes achieving quiet work, and then be done.
A chiropractor never hurts to go to. Even if his body is sound, the chiro can always suggest some stretches or other techniques to do.
"You're just as sane as I am."~Luna Lovegood.