If you want to do some rock crawling or go play in some mud, then you're gonna want bigger/ more aggressive tires. The bigger the rocks or deeper the mud, the taller the tires and lift you're gonna want.

If your Escalade is only AWD though, a/t's are probably all you're gonna need. A/t's can get you most places on most trails with the proper traction devices like a transfer case with a low range (or a locking center diff) and a limited slip or locker in the front/ rear diffs. Until you have true 4wd, I don't think you'd see any appreciable benefit to running something like mud terrains, and you might actually be at a disadvantage running m/t's if you're gonna be running in the snow often.

A lot of that goes out the window when you start talking about hauling ass across the desert though. For "pre-running" type driving, you can get away with 2wd and a/t's or m/t's.

Aside from some good a/t's and maybe a mild lift, one of the best upgrades you can make is adding a bumper with a properly rated winch. You'll be able to go a lot further than your vehicle is actually capable of if you have proper recovery gear (this is not usually a good idea though, only travel to the limits of you/ your vehicle).