A.H.
None of these places have carousels, but they are great places to play in the winter:
Pretend Playground in Mundelein:
http://www.pretendplayground.com/hours.htm
Children's Neighborhood Museum
http://www.roundlakeareaparkdistrict.org/parenttot.html
Little Village Playplace
http://www.littlevillageplayplace.com/
Also, look to see if the gymnastics places in your area have any Open Gym days. Cary gymnastics does this and some of the others do too.
Lastly, Parents Who Care (http://www.parentswhocare.org) do a weekly open gym event where the kids can run and play with a ton of toys in a gymnasium together. They will usually open this up to non-members too, for only a slight increase in the fee that the members pay.
Have fun!