There are many folks who own multiple homes & vehicles in different states. You have only one domicile state, but you can have a residence & vehicle in 50 different states at the same time, if you choose to. The general rule is you register & insure the vehicle in the state where it stays when not on the road. Most state DMV's will require you to show documentation of property ownership before allowing a non-resident to register a vehicle. So you can't just reg a vehicle in a low tax state, without actually owning property in the state where you store the vehicle (unless that state is actually your domicile).
Thousands of NY'ers who own homes in Fla have Fla registered vehicles stored at their seasonal home/condo in Fla. Thousands of Texans have a spare vehicle stored/registered/insured at their part time home in Colorado, etc,
My primary home is in SD and 8 of my 10 vehicles are SD registered, but I keep a Jeep at my seasonal home in Co and its required to be reg & insured in Co; I keep a spare pickup at my winter ranch in NM and that vehicle is registered & insured in NM, etc.
As far as registering by mail, most don't allow it for the initial registration. Some will allow your legally authorized representative to perform the registration, call the county treasurer or DMV in Al. The popular fulltimer states SD, Tx, Fla allow registration by a rep of your mail forwarding agency, with a signed Power of Attorney document from you.
Jim