For my endurance horses, I tend to warm up about 30 minutes when I know I'll be going at least 25 miles at 8 mph, or if the terrain is hilly or technical - even if they are in top shape. The first 5 minutes I literally stand on the ground and stretch their legs out (most of the time they lean back and yawn because they like it) and then I get on and spend some time doing some big/long-strided walking with impulsion (like a flatwalk with a gaited horse). Then we trot for awhile around here/there and are good to go at start time.
For casual riding with friends or around the house (non stressful), I just start out slow and walk/jog along for the first 20 minutes or so as part of my ride, so it works out the same anyway. We always cool down by walking in the last half mile.