I just moved away from Chicagoland. Owned a convertible the 8 years I lived there. In that time, January was the only month I never put the roof down. Every winter has a warm spell in December ore February. With heated seats, the small roof area, and a decent heating system the winter won't intrude too much.

The biggest downside is that there is a huge differnece between top down motoring in the city or a crowded tollway versus out in the country. If you are considering a roadster in December, you might miss it come April - but as others have said you need to do what you want to do.