Great article, Tom! As I read it I could only think, "been there! I can sure relate!"
Warm ups are individual. Bobby Shew's warm up consists of fluttering his chops for a few seconds. He picks his horn up and BAM! Double C - with hair on it!
I've stories of Doc showing hours before a gig to warm up and get ready.
Personally, I can pick my horn up and play pretty cold and squirt out some high notes cold, but I don't PLAY well cold. I prefer a twenty minute warm up if I have to play right away.
On gig days what I do is PRACTICE. I have a gig tonight. I started practicing at 10 AM. I play a lttle and then put it down, play a little, and the go out and cut the grass, play a little and then go work out, etc. By the time I get ready to go to work tonight I'll have practiced about three hours on trumpet and one to two hours on piano. It will appear to others that I'll take my horn ot of the case and play cold, but that won't really be the case. I'm just ready to go.
It really depends on the player and the gig, IMHO.
FWIW coming from me!
Nick
PS: BTW, on days when I don't have a gig, I do the following routine:
PRACTICE!
There really isn't anyu difference, unless I want a day off.