I doubt if you need or want chains, but you certainly do want and need winter tyres (four of them) With lack of experience snow and ice is a serious risk factor. If you start thinking just two winter tires will be enough, or that you can get by without any winter tyres please forget it. Winter driving is not about getting stuck, but it is about being safe. You will be a lot safer with four winter tyres than just two.
I have lived my life in mid Ohio and I use four winter tyres. In fact I expect it will not be long before I am putting them on.
Drive carefully this year. I have had a lot of driving experience in Seattle area and while they do have snows and some really bad hills when they are snow and ice covered, you really need to ease into the weather conditions and road conditions this year.
Good Luck