I live here and can say as the PP stated, we FL people freeze below 70 degrees.

Since you are in the mid west and have had a pretty cold winter so far this year, think of our Jan as your end of March beginning of April. Usually temps during the day are some where in the 50's - 60's with lows in the 40's to upper 30's. We have had a VERY warm winter so far and it is predicted to be wetter than normal so I'd pack a poncho or two just in case. Normally Jan is pretty dry but the weather is a bit crazy this year.
Temps next week are going to be in the 70's during the day so you might even get to swim!

pools are heated at WDW but you won't find us FL people in them.
There are pay lockers in each park if you want to store a jacket. I've done this myself and it was WELL worth it.