I have somewhat mixed feelings on the use of ATVs for hunting. In New Mexico, there are two distinct trains of thought.
In the Gila Nat'l Forest on the west side of the state there are basically no restrictions on their use. This means that pretty much everyone and his brother is out there tearing up the place. I see a serious lack of respect for our natural resources by many of these riders that call themselves hunters. Like was stated above, these monkeys think they need to be on the gas the whole time. Add that to the folks that just poke along with a loaded rifle or shotgun looking for a deer or turkey, and you have a potentially dangerous situation. In this instance, I'd like to see some restrictions placed on ATV use.
On the other side of the coin, in the north (Carson Nat'l Forest), ATV use is restricted to established roads only, no trails or off-road use at all. This makes for a nice quiet hunting atmosphere that I appreciate. However, this benefit becomes a detriment when it's time to get an elk out of a deep canyon a mile from the road in 80-90 degree weather during the bow season. For the hunter that can't justify the use and keeping of pack horses, being able to use an ATV for recovery purposes would enable him to hunt a considerably larger area without fear of losing a downed animal in the heat. I'd like to see an exception to the ban for recovery.
I don't own an ATV, but wouldn't mind having one to facilitate travel between camp and trailheads and to help hump out the critters. However, I recognize that we (as hunters and/or riders) must respect our environment and the wildlife that lives there. Unrestricted use of any vehicle has a significant negative impact on the outdoor experience. Based on my experience, we (big umbrella) can't be counted on to use ATVs responsibly, so I see the need for some official "infringement" before irreparable damage is done, both to our beloved wild places and to our images.