Casual play I usually stretch at home and then proceed to the course. If I did not stretch and there is time and a place on the ground that is not wet/muddy I will stretch at the course. Then a bit of putting. Almost never hit balls other than courses that may have a chipping area.
Tournaments, I am typically working the registration desk and I am lucky to have time to putt a few and stretch. If I am not tied up with administrative things, I will hit a few balls. I like to see how my driver is behaving (a bit of a fade or almost straight is my standard flight) so I can anticipate whether to aim at the left side of the fairway or right.
This weekend we had a very slow round. One of the guys in my group has back issues and was putting a swing donut on his driver to try and stay loose while waiting on the tee. Another in the group said it was a rules violation. I looked on my phone but the closest thing I found was he could not take a shot with any kind of training aid, but nothing mentioned using them during down time in a round. Did I miss something or was it ok?
My routine is the same for both casual rounds and tournaments: 20 minutes on the range and 10 minutes putting. I know from experience that trying to warm up for longer for tournaments than I would any other day just gets me out of my comfort zone, which is huge for tournament play.