I'm from Chicago. When I didn't ride a bike, I used to think that Chicago had miserable weather 11 months of the year. When I started riding a bike, though, I noticed that the weather is generally great from March-November, 9 months a year. Not riding your bike 3 months out of the year is much better than avoiding it 12 months out of the year. (FWIW, December-February isn't really that bad, it's just not enjoyable. You'd be surprised how non-cold you are once you start moving.)

Also, I am confused as to how riding the bike in the rain is dangerous. Some of my most enjoyable rides are on rainy days. Instead of getting wet and salty from your own sweat, you just get wet.