I think 3 or 4 places with a month in each is perfectly reasonable. It's a good way to find where you might want to return for a longer stay. As a tourist (which is what you're going to be, not a typical snowbird) I don't think you should be afraid of the cold weather warnings in the south. Yes, you might hit some below freezing temperatures in New Mexico for a few days but you weren't planning on sitting in armchairs basking in the sun were you?
We've snowbirded in Florida, RGV and Arizona. Each has it's advantages and disadvantages.
We've left Ontario in beginning November to tourist Florida then to the left coast and up the coast to the bottom of Alaska and back home by the end of May. We really enjoyed that trip but I don't want to do that every winter.
We normally don't leave Ontario until late November. The biggest issue is lake effect snow. You shouldn't have too much trouble with that as it's usually to the east of the lakes. Don't be afraid to park for a day or two to let a storm system pass.