The horn, though, is a different beast altogether, and not warming up properly can have huge downsides in simply not being able to play well or for very long. This post by James Boldin is a good one on some of the issues of horn warm-up.
Reading and thinking about James's post lead me to remember that the "warm up" for Buddhist spiritual practice, whether attending a dharma talk or a solo meditation, is reviewing and "setting" the motivation. In most of what's been written about musical warm ups, the focus is on the physical aspects. Taking a little time at the beginning of each practice session to think about what you're trying to accomplish, and why you're trying to accomplish it, can be valuable as well.
Physical technique is very important, but there's a lot else involved in making music, and calling some of that to mind at the beginning of each practice session can bring more balance of all the elements to the endeavor.