I camp a lot on Mt. Lemmon outside of Tuscon and they cut a lot of trees down on their own, thing is they don't make it into campfire sized logs for you. I believe its listed as a National Forest but I'm not a 100% on that, I'll check when I head up there Friday. Perfectly legal to burn the stuff they cut or the deadfall there, and a good chopper is very neccesary.
There are places like the Grand Canyon where its kept so tidy you won't find any deadfall, at least that's how it was around 5 years ago. Pretty much have to bring your own wood along there.