You don't need to play a concerto to play musically. You should "switch on" your musicality right from the first note of the day.
When I warm up, I think like a singer doing scales and arpeggios and it makes everything much easier.
You probably play more or less the same things every day to warm up so it's easy to become mechanical with it. The musical energy you put in your warm up will help you reach the notes and prepare you well to play your excerpts, etudes and concertos with great musicality once you've completed your warm up drills.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.