There are going to be compromises that you need to be willing to make, since there is no perfect place (that I’m aware of), as a family it might be worth sitting down and discussing and looking at areas on the computer together.
Florida has a big horse scene, good vets, farriers, trainers etc. If you feed anything other than Coastal Bermuda you will pay up to $30 a bale for hay, that’s two string bales. Taxes aren’t bad in some areas but you better love hot humid summers and the chance of hurricanes or tornados. Plenty of bugs, snakes and gators too.
The Carolinas - this weeks news should about cover how it can be to live there unless you are well inland. Tyron might be worth a check. Summers can be humid though and a chance of snow closer to the mountains but not bad winters per say.
Phoenix and Scottsdale are pretty if you like desert, blazing hot/dry summers mild winters, no real bad weather other than occasional dust storms. Think they have a winter circuit for horse shows.
Texas is nice, love the Austin area; however, it’s congested, expensive and not sure about the horse scene there. Denton TX has a big horse crowd though likely more western. They do get tornados and some bad winter storms otherwise not bad.
Research each state on their public schools and how they rate.