Snow is hard to bike in (I think, I dunno though, being in coastal California).
I’m sure it would feel like a lot to you, but Chicago doesn’t really get a lot of snow or ice. Prevailing winds in the winter are out of the northwest. The majority of the moisture picked up from Lake Superior gets dumped on the Upper Peninsula and Wisconsin before reaching that far south (Lake Michigan moisture is dumped in western Michigan and northern Indiana).
Biking infrastructure in Chicago is good in wealthier areas and pretty bad in poorer parts. There is definitely an element of unequal funding, but you have to understand that Chicago’s municipal system of government puts a lot of power at the hands of the alderman - they are like little mayors of their wards. If the people in a ward want bike infrastructure, the alderman will find the money for it. If the people in a ward don’t want to give up car lanes for bike lanes, it’s not going to happen. And that’s how they feel in the poorer areas. There have even been instances of bike lanes being removed in some neighborhoods!
It's flat and - at least north of the Blue line - there's good infrastructure. Combine that with dense population, and the lake and tons of parks nearby, and it's the best biking city I've ever lived in.