Walking through many national parks in winter can be tricky. In Yellowstone National Park, for instance, the boardwalks through geyser basins can be snow-and-or-ice-covered, hiking trails in Grand Canyon National Park can be icy, and trails in countless other parks that experience snowy winters can be slippery. These are definitely instances when you need good footing.
If the snow is deep, snowshoes with crampons will provide you with great traction. But if the trail has been compacted by lots of feet, snowshoes might not be the best answer. Instead, I've found that YakTrax are a great solution. Made of rubber or plastic (depending on the model) and 1.4-millimeter coiled wire, these stretchy "traction devices" fit over the sole of your footwear. The coiled wire that runs along the bottom bites into the surface of snow, and ice to a degree, to provide you with some grip.
YakTrax fit over hiking boots as well as running shoes if you want to head out for a run in the park for your exercise.
There currently are two versions -- the $20 Walker and the $30 Pro. I found the Pro to be a bit more durable than the Walker, which I managed to quickly break while stretching it over my size-11s. Not only is the Pro made from a beefier natural rubber, versus an "injection molded thermal plastic elastomer" for the Walker, but the Pro also has a strap that fits over the top of your boot/shoe to help keep things in place.
And for those really cold days, the manufacturer says these devices will work in temperatures to minus-41 below zero Fahrenheit.