Sure, you CAN plow with a warrior, it's probably the best built sport quad for the job because so much about it seems utility-ish. I think the biggest issue would still be that it's 2 wheel drive and that usually isn't the greatest for plowing, it'll be totally useless if there's a layer of ice under the snow. All that extra weight on the front end from the plow means there's less weight in the back keeping those tires planted and holding traction. Studding the tires and throwing some chains on might be enough to get it to go anywhere, but I'm not sure of that so if it was me I wouldn't take that chance. I think you'd be better off with an old 4 wheel drive, something like a honda rancher. They're great workhorses and would probably plow through a volkswagen if your plow is strong enough.
I never rode a sport quad with studded tires and chains in the snow though, so it might be enough to plow. BUT if it isn't, and you're spinning your tires all the way across the driveway while you're plowing, people are gonna be pissed when their driveway melts off and dries, and there are chain tracks and gouges all the way up and down their driveways. I've seen that before with somebody plowing with a 2wd moto 4, but the kid was a dumbass, basically plowing 3rd gear pinned. I'd keep that in mind.