Back when I used to climb many moons ago, I always wore chaps in the tree if I was running a saw. I figured, of all the times to get cut, that would have been the worst place. But I was climbing with spurs and a belt, not much gear, just a pass rope and tag line for the saw and to haul crap up when I needed it.
I never cared for the full down wrap around the calf style, I just wear chaps that cover my thighs and about halfway past me knees. They make kneeling a lot more comfortable, you can fold them and sit on them at lunch time, put your hands behind them to warm them up, easier than pockets.
I always said if you're bouncing a saw chain off your leg, chaps are not the cure. But I've seen some highly experienced, professional cutters catch their chaps a few times. 50 years running saw, never cut my leg or my chaps. Still wear them, you never plan to cut yourself but it's not impossible that you will.