The bottom line of what a warm up should do for a horn player is to make oneself comfortable.

Ask your self what it is I need to do before a gig to make me feel ready to perform and comfortable.

Arriving early to a job is important. Take time to get your horn acclimatized to the space. Test the room, limber up, get in tune relax a little, but also . . . .a warm up needs to remind ourselves of our best habits and do some work towards improvement.

Don't forget to work on BREATHING! And contrasts of many kinds.

I am a huge practitioner of the philosophy do a little each day.