Well, I'm coming late to this party (I was on vacation with you first posted) but I must add my own
Welcome to Alabama
I live just east of Birmingham. The weather is nice, the traffic isn't too horrible, and the beaches and the mountains are within a day's drive.
When I was nine, people from Michigan moved next door to us. I used to go play with their kids and come home with thier accent. Mom would tell me to "stop talking like a d. yankee." LOL

30 years later, they still live next door to my parents and are their dear friends. I'm sure you will like it here.
Without repeating too much what others have said...
Snow - My younger dd is 8 and has seen snow only twice in her lifetime. "Snow" being some scattered flurries that you can see if you turn on your porch lights. Sometimes it will stick in the grass. If it sticks on the road, then yes...everything will be closed. Sometimes just the PREDICTION of accumulation will result in closures. The true problem is that it can get warm enough during the day for it to melt a bit, then it freezes over again and you have ice. Nasty stuff. And don't go out driving in the snow if by some miracle it actually snows, because you may know how to drive in it but we do not!
My kids never wore their winter coats last year. Some years it does get cold, though.
Make sure you keep milk and bread (or whatever you need to eat and drink) around and when snow is predicted don't go NEAR a store! Yikes! You'd think people were stocking up for Y2K again
Speaking of grocery stores, we have buggies not carts
Gulf Shores/Orange Beach is a wonderful family vacation spot. No one has mentioned the awesome outlet mall just inland.

Great deals!
Lots of houses have basements. I don't think Montgomery is a big tornado-prone area but basements are good to have
Y'all slice your watermelons differently than we do.
We don't drive the speed limit, we drive the temperature.
You're only about 60-90 mins away from Birmingham (depending on which side of Montgomery you are on) if you want to visit here. The zoo is nice (Montgomery has one too, but I've not been there) and the McWane Center (children's science museum) is really fun. They have a separate area for kids under 5 that my girls both LOVED as preschoolers. They have an IMAX theater as well. The Birmingham Museum of Art is quite a decent museum if you like such things, and a little further north, the Space Center in Huntsville is also very cool.
If you like outdoorsy stuff, there's plenty to choose from there too. Most of the State Parks are very nice.
http://www.alapark.com/
There are also world-class golf courses, if you're into golf
You won't be that far from Atlanta either, if you need a "big city" for shopping or theater. The Aquarium in Atlanta is supposed to be really incredible (I get to find out first hand soon - older DD is going there for a field trip in April

)
Once again, welcome to our fair state, and
WAR EAGLE!!!