I don't have an ATV but I really don't see any advantage of one over a Tractor.
I've got 2 tractors, one a good sized compact Deere (43 hp) with a grapple, bucket, flail mower and tiller. and a small old wheel horse ( think old lawn tractor) with a 14hp Kohler engine. Contrary to what others say here I use my old wheel horse in the woods for getting wood. Its smaller, easier to get around. I pull a small trailer that I load with wood (it'll carry more wood than the big tractors bucket). The wheel horse has chains mounted on it at all times. I have never got stuck with it with only 2 wheel drive. I have got it to where the tires will spin. I then drop it in low range maybe 1st or 2nd, let out the clutch and while the tires are spinning I jump off and give it a push. once its moving on its own I get back on and away I go.
And far as pulling logs out with the tractor, I don't like the idea of loading a log up with dirt then running a chainsaw thru it. I drop the trees and saw them up to lengths right where they fall. I drive the small easily maneuverable tractor right up next to the wood and load up the trailer and I'm on my way back to the splitter and stacking.
I can't imagine mowing a yard with the Deere. I do mow a couple of acres of field that I am restoring to tallgrass prairie at times but its not a delicate thing. No way I'd use the big tractor for my yard. Too many ruts and tearing up the turf.
On a side note if I had 3 acres of lawn I'd look at letting it go back wild and only mowing 1/4-1/2 acre of lawn at most.
I think yards are a waste of potential wildlife habitat, nothing so foolish as living in the country and having a yard that is several acres big. Better it is wildlife habitat, a couple of acres of well managed good habitat will support lots of rabbits. More fun in having a rabbit hunt on winters day than spending many a summer afternoon on a mower. And you get a rabbit dinner out of it too.