The best warm-up exercise that I even still use today and have done for a long, long time is to, well after getting the reed wet, moist, usually with a cup of water is to practice long tones.
It gets the reed working right because the reed's wood, it changes with moisture. Gets the muscles warmed up and really gets your ear in tune with playing a note in tune.
The long tone exercise I use is to use a whole load of lung capacity to move between two notes. So, I want to use a whole breath to move from B to B flat.
Then I'm going to do the same thing from B flat to A. All the way down the horn. All the way back up to B. And if you've never done that before by the end of that you feel like you played a three hour gig with no breath. Your muscles are really, are really sore.
And it's a great endurance builder and a great warm up exercise. I still use it today.