Actually snowbirds also come to the Texas Gulf Coast.Only the folks from the Eastern half of the US go to Florida. As you mentioned, Westerners go to Arizona.
As far as a Snowbird goes, I'd be the opposite. I need my seasons. Summer in the tropics of Florida or farther South - swimming and fishing; Fall in the Northeast - leaf peeping, pumpkin and apple picking, and hunting; Winter in the snowy mountains, fur skifahren.
Spring is optional.
I haven't heard of many people going to Phoenix in the summer. Now Sedona is another story because it is in the mountains and cooler.