I've been in the Twin Cities proper my whole life.
The high temperature here for the next 10 days will be around 5 degrees (Tuesday, next week). It's the longest cold stretch since 2014.
I got a cousin in FL - there is nothing really keeping me anchored here anymore. So I will be able to go wherever I want I guess - in theory I could leave tomorrow.
although I never lived in AZ, I did visit is often about 10 years back. I visited in each "season" (well, during hockey season). Obviously it's spectacular in Dec/Jan when I mostly visited). I did visit once in the summer (June or July) just for fun and while it was hot, the low humidity was much more bearable (I grew up in Eastern Iowa).
In terms of other possible locations to move to (if AZ doesn't work for you), I completed my student teaching near Seattle (Aug-Dec) and it was awesome. The benefit is that you have everything within 2-4 hours (high desert, rain forest, mountains). After living there, I determined that I would retire to WA; unfortunately, with climate shifts, it may not be as appealing these days (I was there around 1997). It did rain more than Iowa, but it wasn't too bad for me (I don't mind rain)
Currently, I live in southern PA, and like it. It's similar to Iowa, but much less harsh winters (I believe we might have gotten down to the teens once this winter so far--we have hovered around the mid-upper 30s and low 40s mostly this winter), I've lived here for about 12 years and I think we only got down to negatives once or twice (and only for a few days--"low" negatives that is--around -9 or -10 but without active winds). We do get a fair amount of snow (compared to eastern Iowa), but it is typically only 1-2 major storms a season (I ended up with around 10-12" of snow last week--the only major snow this season, again so far), but temps make it more bearable to clean up and still go about a relatively normal life.
I've lived in IA (mostly grew up there), WA (6 months), GA (~4 years), IN (1 year), NJ (5 years), and PA (~12 years) in the last 25 years and definitely prefer PA (feel free to ask me about any of the other states if you'd like). My advice (given your situation--if there is no rush) is to pin down a few places and visit them over the next couple of years at various seasons (if financially feasible) and then decide. If you have to make a decision soon, AZ is pretty safe bet (decent cost of living, plenty to do, and drive distance from various potential road trip options.
PA is pretty good as well (depending on your age/interests), but the cost of living is higher than AZ so keep that in mind for salary info. GA has a low cost of living, and plenty of social and occupational opportunities (my brother lives there), but is similar to FL in terms of weather (GA doesn't get quite as humid). I envy you in your journey. I have applied to AZ for a few jobs over the years, but haven't received much beyond one phone interview (probably due in part to distance since my field typically helps pay--or fully covers--travel for final candidates). Of course, at this point, I'm hoping to retire in 10 years (if feasible), so AZ is off the list presently, but I'll revisit it in 5 years.