Chicago is a first-rate city, very comparable to NYC or a major European city, with a significantly lower cost of living than Singapore. You'll be able to rent something comparable to Singapore for less than half the cost, and buy for 25-33% the cost. It's an amazing place if you're looking for a busy first world city.
Downsides? Frigidly cold winters. Summers can be comparable to Singapore. Spring and Autumn are very mild and pleasant. Seasons are erratic, so Spring may start in February and Winter return in April
Traffic is significantly worse than Singapore's, but not as bad as a third world like Jakarta or Bangalore. (but if you do miss Bangalore/Indian driving, drive to Devon and Western on a Saturday afternoon)
After tax salary is the same, you're sure? You're including state income tax, etc? You can use
www.paycheckcity.com to calculate your local after-tax pay.
I am wondering whether I will be able to survive the weather and cost of living if I move.
Keep in mind that just like everyone survives Singapore via A/C, everyone survives Chicago via staying inside with the heat on. Heated cars, heated everywhere. You put a coat and hat on, and you're fine. You walk to the car, you park, you walk to the place you're going. Unless you're spending significant amounts of time outdoors in the winter without proper clothing you'll be fine. Millions of people do it all the time.
As for cost of living, as I mentioned above Chicago is way way cheaper than Singapore. Some of the most posh areas of the city have
condos for less than $500sgd/psf. And we're talking units with views of the lake off the Mag Mile (think Orchard Rd, but actually and not fake upscale). If you live in a suburb and commute in to the city, your psf will be half or less of that even.
Here is a comparison from Numbeo, but I would argue you can save significantly more in Chicago than even they claim due to its diversity and vast scale of available realestate:
http://www.numbeo.com/cost-of-living/co ... cago%2C+IL
Anyway, I was born and raised in Chicago and would gladly give you opinions on where you're looking (it's a large and varied area). Where you intend to live and work is important.