I drove mine all last winter with a set of snows. Other than the Oct storm where it spent about a week hiding in the garage while I let my wife’s Expedition get beat to shit by tree branches the GTO always got me to work.
I’ve always been a proponent of the idea that all season tires are good enough for Buffalo winters but this car changed my mind. A 245 performance biased all season is WAY too wide for snowy roads because it can’t cut through the snow to get traction on the pavement. The car was downright dangerous if there was any snow on the roads with the stock BFG KDWS’s. And talk to anyone who’s seen me autocross or drive at a track day; I’m not one of those idiots who doesn’t know how to countersteer. I’ve been called things like “captain slideways” and “dirt track racer”. 
With a set of snows the car wasn’t bad at all. The factory traction control is extremely aggressive so with that on (it’s on by default every time you start the car) and decent tires it’s hard to get into too much trouble. It’s still 400 hp, in a rwd car, so you have to respect it in the snow but it’s heavy enough that I would rank it well above my old 2WD V6 open diff Ranger in terms of snow capability.
Oh, and prepare for the majority of the idiots on boards like LS2GTO to act like you just kicked their mom’s in the face when they find out your GTO has seen salt. They seem to think these cars are 100k+ exotics or that they’re going to be worth mega-bucks as a collectors item in 40 years. I bought mine to drive it. I still get people who tell me to buy a <$1000 beater, but I don’t see myself driving some POS just so I can keep my much more fun to drive GTO sitting at home in the garage. If it was something rare I wanted to keep forever like a Ferrari or a 911 sure, but a GTO is “just a car”. When it gets up there in miles I’ll trade it on something else I can drive every day that’s fun.