I'm in Mich. and I did my first winter riding a few years ago with a badly used Walmart MTB. No serious problems.I just used regular knobbies and didn't have any additional equipment. Just buy a better bike (MTB or other type--whatever) if you find yourself loving riding. As somebody said, "It isn't about the bike."
Personally, I think your next investment for winter riding would be a headlight and red blinky, as winter almost always means darkness while you're riding. You can put off other purchases until you're ready for more.