I like snowshoeing. Since my kids were very young, I bought them snowshoes. It is an easy family activity you can do together and it doesn't require a lot of effort or time. On a Saturday when Emily was skiing at Brighton, Brennan and I took a day to snowshoe. Silver Lake is a wonderful place in the summer to bring kids with easy walkways and plenty of wildlife located very close to Brighton. In the winter, it turns into a cross country ski/snowshoe paradise. For a small fee, you can use your own equipment and take advantage of all the marked snowshoe and cross country trails. It is run by Solitude Nordic Center and there are also snowshoes and skis to rent. If you have never tried cross country skiing, you can also sign up for lessons. Definitely on my bucket list for this winter.
On this day Brennan was less than excited to snowshoe, so I had to make it fun. I bought snowshoes last winter from Costco for the kids. They are inexpensive and came in a bag with poles. One bit of advice, use only one pole with the kids as you will probably end up carrying them by the end. Get ones that have quick snaps so you can tighten and pop around the back of the boot. For kids, you don't need to go with a high end snowshoe as their feet grow too fast. A little crampon-metal, claw underneath-is fine as you will not be doing big mountain climbing at this stage. Also, regular snowboots are just fine. Most of the trails have a gradual slope and are very well marked. Bring a backpack with water and a few snacks. We grabbed a map and all the trails are color coded and named. When starting at the Nordic Center, you can go all the way to Solitude on your snowshoes.
In order to avoid "This is boring, when are we going to be there", we play games. The alphabet game is awesome for kids, and we do this even when we hike. One person starts and says "I'm going snowshoeing and I'm going to take an apple." The next person goes and says "I'm going snowshoeing and I'm going to take an apple and a ball". It goes from there through the alphabet and it not only keeps the kids occupied, but you are building on their memory as well. When we get in the car, go on a hike or anything that is active, Brennan automatically starts the song. Another thing we did was to build a snowman. In this case, it was Olaf from Frozen. It broke up the walk and turned into a hunt for the right pieces to put the snowman together. You can listen for wildlife, identify trees and make it a great outdoor experience. By the end, Brennan said to me "This actually was really fun!". Mission accomplished!
There are tons of trails in the Wasatch, and a lot of them are very close to the ski resorts if you decide to take a day off from skiing and explore with the kids.