This time of year it is difficult to combine these three elements. It's the time of year when cooler weather makes kids and parents want to stay inside where it's warm and play more sedentary games.
While board games, computer games, electronic games, even interactive electronic game systems can be challenging, educational and involve some engagement in physical activity, nothing compares to the health benefits of fresh air and exercise while having some great outdoor family fun.
Some activities that ignite excitement to get out and play are bike riding, scooter riding, ice skating, snowshoeing, cross country skiing, sledding, tubing and just plain hiking.
Obviously, you have to have snow to go sledding, tubing, snowshoeing, and cross country skiing, but these are all fun family activities. If you are a city dweller with no snow slopes or snowshoeing or cross country paths close by, go to the city park and pull the kids on sleds, have a snowball fight or build a snow fort. Playing soccer or football in the snow is also fun and adds a challenging dimension to both games. In any case, for a day in the snow you need to dress warmly, pack extra mittens and outerwear, and make sure that the trip includes hot chocolate either in a thermos to enjoy during your outing or as a culmination trip to your favorite hot chocolate vendor.
If you live in a more temperate climate that rules out playing in the snow without a trip to the mountains, some family outdoor fun can be had by planning a nature hike or bike ride that might include a favorite playground either on the route or as the end point activity. A trip to a local roller skate/scooter/skateboard park with age appropriate ramps and skating/scooter paths can also be a fun activity. Some areas that enjoy milder winter temperatures also keep their miniature golf parks open during cooler months and it might be a fun stop on your hike or bike ride.
During the Christmas season, many cities have a lighted fun park. These parks usually include lighted paths to follow as well as an area for the kids and adults to freestyle dance to traditional holiday tunes. Often, there are vendors on site with hot drinks to keep the body temperature up. Some cities have free sleigh rides and/or horse and buggy rides in connection with their lighted parks that add to the gaiety of the season.