We uprooted and moved states twice with a little kid - once when she was 5 and once when she was 7. It is true that children are remarkably resilient and many make transitions easily, make new friends, and hit the ground running.
My young'un isn't like that. She's an introvert, and she grieved the loss of her close friends both times we moved. In fact, the second move was in the hope that it would be the last move and we would not have to uproot her again during her childhood.
I still think we did the right thing making that move when she was 7, but my opinion is the younger the better, before they've established roots in schools. If you're thinking of moving sometime, say, in the next five years, I encourage you to look at sooner rather than later. Each year a kid spends in a school, they dig deeper roots there.
You probably won't find "warmer" if you're looking at CT, NY, or Maine... were you thinking of moving closer to family?
Land is cheaper in the South, and it's warmer, for sure. But it's a long, congested, unpredictable drive to see family, even if you chose Maryland or Delaware (mid-Atlantic more than South). We drive from PA to NC three or four times a year, and we dread the drive each and every time.
So my advice is to consider whether there's a place you could move that's in relative proximity to family, where you could afford to buy a piece of property where you could garden, raise backyard chickens, etc. You don't have to have a "farm" per se - a couple of acres might provide plenty of space for what you want to do. And make sure the school system is decent in a place where you can afford to buy land outright. That combo might be hard to find in the pricey Northeast.