Short answer: Yes.
Long answer: Well, really only in winter. It snows significantly more, and it gets significantly colder. January/February in Madison can be really depressing and awful, but from what I've seen of friends who came from other places, they acclimated after the first winter.
I've carried a shovel in the back of my car since I was 16, because you will get stuck in a snow bank, or a friend will get stuck in a snow bank at least once a year. I drive a lot out in the country, so I was at a little more risk, but Madison has a tradition of not salting the roads enough and not plowing until the street has frozen into a block of ice.
Summers will probably be easier for you, but we still get hot and humid. Fall and spring are spectacular.
Since you're midwestern to start with, I don't think you'll have a horrible time adjusting. Just have a nice and warm winter coat and be ready for the seasons to be very very well defined.
I'm writing this from my new home of Columbia, MO, and I am dying in this heat/humidity. I am like a polar bear in Florida right now. Guhhh.