If you want a bunch of starter snowshoe trails to try-out all on one place and something close to Thunder Bay, then Hazelwood Lake is the place to go. There's the Dam Trail (725m), the Forest Community Trail (1.8 km) and the Orange Trail (2.2 km). Click here for larger PDF view.
Centennial Park is another close option for trails in Thunder Bay. For a more details we would recommend going to Wayfind: Trails & Recreation's website, a local Thunder Bay company creating trail maps so you don't have too.
A longer drive to get there, with a 4.2 km full loop trail. Above is the winter snowshoeing map in the Whiteshell. Click here for larger PDF view of trail (bottom left) and even more snowshoeing trails in the Whieshell.