Welcome to the Forums, KC10Chief.
Studded tyres make all the difference, especially in the conditions you described (ice, hard packed snow). For studded tyres in USA & Canada, an often mentioned source is
Peter White. He has a good selection and also articles on studded tyres.
For me, Nokian studded tyres are locally easily available and relatively cheap. For a while they were also the only studded tyres with durable carbide studs, but now at least Schwalbe is following the suit. Durability is important in daily use, and also in the sense that you can ride over clear patches of pavement without worrying for your tyres. I have a pair of Hakkapeliitta W106s permanently mounted on my winter bike for commuting on road. For winter offroad you'd need something with more studs and more aggressive thread. For the entire Nokian product range, see
here.
As you noticed, you'll need good lights too. There's a lot of discussion on various different types, power sources etc. in our
Electronics, Lights and Gadgets -subforum. And of course, there's the whole
Winter Cycling subforum, although it's somewhat quiet right now. But just wait until autumn...
Winter biking is an entirely different sport - there's a lot of rolling resistance from snow, studs and lower PSI. You may have to invest some money in winter clothing. Exercising in cold air might be new to you and require a bit of getting used to. But it's great fun!
--J