Based on where you live in central Ill. you get roughly the same snow fall as we do in North Central Ohio. I looked up the averages and Ill. gets 38 where Ohio gets 28. But Northern Ill. probably makes your snowfall total higher and my snowfall, one hour north of Columbus, is always higher than everyone in Columbus. We usually get about twice the snowfall they get one hour South of us. We are in kind of a snow track.
That said, and having owned almost the exact tractor you own, (MF GC2400) just a few years older. Since you don't have slope, you do not need chains. They are expensive and they are a pain to put on. I've run chains on other things.
What you will need, and this is a certainty if trying to push much snow, is rear ballast. Tires being filled does not give you enough ballast to push snow with industrial tires.
You need to look on FB marketplace or CL and find a used Dirt scoop or ballast box. You can pick up a dirt scoop for $200 if you watch. I like the King Kutter (AKA Country Line or Tarter), since they weigh almost #300 empty. Put three bags of sand in it and you are #450. For less than $220 you have your ballast and you have a bag of sand if you get stuck : ) Don't worry that they are crusty, they can be sanded and painted whatever color you like. A new will cost you $700 so don't do that. When empty the are easy to slide around or move with forks. In summer, they can be used to carry tools, equipment and supplies to a work site and just keep on the tractor for ballast for loader work. Every compact or SCUT should own one IMO.
They are fairly low footprint for storing and for when they on behind your tractor. You do not want a 4' wide implement on the back when pushing snow, unless it is a rear blade which you can use to push snow.
Here is an example of the KK and it has been out there a long time.
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