Even in the winter, there is still plenty to do in Colorado other than skiing or snowboarding. Just keep in mind that the weather can be drastically different from one part of the state to the next, and although it's 65 and sunny in Denver, it could very well be 15 and snowing by the time you reach Loveland Pass. Always check the weather before heading out and keep in mind that highways may close, especially over the high passes, in inclement weather.
Hiking in Colorado during the summer and fall is a great adventure, but once the snow begins to pile up the exploring doesn't have to end. Strap on some snowshoes and you can get out and explore Colorado in its wintry bliss. There are trails for every ability level, so even if you are not an avid hiker, or accustomed to the elevation, you can still easily give it a go. Best of all, it is very affordable.
There isn't a much better way to heat up on a cold day than to take a dip in one of the state's numerous natural hot spring fed pools and baths. These springs can be found all across the mountains and typically stay at a pleasant 90-110 degree temperature, even in the winter. Its never too cold to go for a swim outside.