A few years ago I was in your situation, negotiating where in the US we wanted to eventually retire. In the end our compromise was NH, and last year we bought a house there, although I have yet to retire.
Deciding factors for NH were:
Gun friendly
Low taxes
Topography (we like the mountains)
Rural
Socially moderate
High quality health care (Dartmouth, MGH)
The only negative IMHO is high property taxes, although overall tax burden is low. FYI, property tax rate varies significantly throughout the state.
Over several years we made multiple trips to NH, vacationing in different parts of the state in summer and winter. Different regions of the state have their individual and varying personalities. We choose the New London area.
The law regarding shooting on your property (from memory) is you must be > 300ft from a permanently occupied structure and can't shoot across (? near) a road. Some developments have there own covenants, so check for those as well. Having gun friendly neighbors is helpful, and one of mine is not, but this is hard to determine while house hunting.
Regarding the winters: we currently live in TN and it is currently 61 degrees, although that is unseasonably warm . However, in the summer we have months of hot humid weather. So pick your poison regarding cold winters or hot summers.