Nope, splitting green wood is much more difficult than splitting dried logs, so I often cut a tree in the spring, stack the rounds, then split those rounds in the fall.
People overestimate how dry wood needs to be to burn correctly. Just have some ultra-dry kindling (seasoned for 2+ years) and you won't have any problems.
On the contrary, I know some folks who let all their wood dry too far, and it burned way too hot and ruined their stove (and almost burned their house down).