I'm always on the lookout for dog friendly hikes near SLC. After a morning of driving around and following shoddy directions, we almost gave up. Millcreek canyon has tons of dog friendly trails, but on the weekends it is extremely crowded. A quick Google search later, we found some interesting sounding hikes in American Fork Canyon - apporx. 25 min from Salt Lake. I have been to AF in the summer and fall, both gorgeous times to visit, but hadn't been since snow fell.
American Fork has a $6 day use fee unless you have an interagency pass (seriously, everyone needs to get on of these). We drove up the Canyon veering to the right on the Alpine Loop. Eventually you will get to a gate marking the road closed for the winter. Park in this parking lot and the world is yours! We were originally looking for Pine Hollow trailhead, but opted to walk the snow packed road instead.
Even though the parking lot had about 10 cars in it, we only passed by another guy with a cute dog! There are some great views and you can walk for as little or as long as you like. This road is also great for nordic skiing (actually American Fork Canyon has quite a few xc ski trails), fat biking, and snowmobiling. Best of all: no snow shoes required! I'll definitely be back to explore more of what American Fork has to offer in the winter.