That really depends on where/how you plan to keep the chicks during the cold of winter. I see that you're in Illinois, so I'm assuming that your winters are very cold, so your chicks would have to be kept in a heated, non-drafty area until the weather warms up in spring. If you can provide a suitable place for them to brood, then you can hatch chicks all year 'round if you want to. I actually kept a batch of the little fuzzies in my living room in a very large horse trough with a heat lamp over the winter a couple of years ago. It got pretty dusty in there, but the chicks were very happy, very tame, and very spoiled!!!
Yep, that's a great place to keep them. They don't have to be inside as long as they are kept at the correct temp, etc. It's nice to have them inside in the winter, though, so you don't have to slog through the rain and snow to care for them. Besides, it's easier to spoil them that way!!!! LOL
Iowa here. I'm setting up a pen in the basement. Just depends if you mind having chickens in the house all winter or if you can setup several heat lamps in your coop you could probably move them out in feb. I usually end up keeping mine in the house until about 8-10weeks anyway. If my eggs hatch in 2 weeks and I keep them for 10 weeks I'll be about to jan anyway. So only an extra month or 2.
Your problem might be finding eggs that aren't overly chilled at this time of year. Especially if you get them shipped to you.