1. Go hiking anyways. Sure, the weather stinks. There could be snow on the ground or rain pelting from the sky, but you can still make going for a family hike a weekly event. It could be an urban adventure, exploring the local trails, or a stroll along a winter beach, but get them out and get them walking. Last winter we had a regular Sunday hike with another family whose kids are close in age to ours. Kids always seem to hike farther (and with less complaint!) when they have a friend along. Some families choose activities like GeoCaching to keep kids interested in moving along.
2. Get to the pool. If you are already a member of a YMCA or local club, make it a habit to get to the pool at least once a week. Forget swim lessons, just get in the water and play with your kids. Bring balls, diving toys, torpedos, or other things to keep the fun and energy going. Most indoor public pools have wintertime family swim hours, and some even have fun activities like movie nights where you can swim while watching a movie projected on the wall. Instead of going to a sit-down movie, make Friday night a family fun night at a local waterpark or pool.
3. Play Indoor games. Especially when kids are little, you can keep them busy with games in the house: Hide-n-seek, tag, pillow fights, wrestling on a mattress, building forts are all perennial favorites. When my kids were smaller, I used to build them obstacle courses around the house with sections like "cross the hot lava" (pillows as "stepping stones" across the "lava" of the living room rug). Take some chalk in the garage and make a hopscotch or foursquare area on the garage floor. Get creative and watch your family grow closer while the kids have a blast and get some exercise in the process.
5. Take a class with your kids. Community centers, YMCAs, Yoga Centers, and Martial Arts schools often offer classes that both parents and children can take together. I've been taking Karate with my kids now for five years. We started out as white belts together and have encouraged each other as we grew in skill and experience. Now my 14 year old is a brown belt who is hoping to test for his black belt next year, and my 11 year old is a green belt whose self-confidence and physical abilities have blossomed in our family-friendly karate classes. Best of all, it's something we did together. They could see me struggle with the difficult moves and came to realize that just because a lot of things look like they're easier for big people, we have to work at it just as hard to get proficiency. It's important for kids to see adults take on new things and maybe even fail (a favorite family story is when hubby forgot his kata in the middle of his test for his blue belt). The kids love to know that we struggle too, and it encourages them to try harder when they see us put in the effort alongside them.