Axe is handy, but makes for exhausting work here in Michigan. You get into the big woods camping and a wind storm developes overnight...you may cut through the first few trees with ease...but after about twenty or so...and your arms will be wishing they were holding a chainsaw. For those that don't carry a chainsaw, best time to wheel/explore is in the fall, after the bear hunters have cleared most/all of the trails (while running their hounds).
Sure you can probably travel some of the major trails year round, but for the trails less traveled...you'll be turning around a lot. And, in my opinion...that's not what I'm out there for. Backtracking/turning around is painful to the "get-where-l-intended-to-go" mindset.
Brian.