Tug of War
Tug of War works much the same in winter as at any other time of year, except that on a snowy day you can add a twist. Prior to starting this contest of strength, everyone can pool their efforts and build a wall of snow separating the two pulling teams. This adds the fun of watching the tuggers at the front of the losing team crash through wall of snow. All you need to play is a length of rope.
Snowball Target Shoot
A game like the Snowball Target Shoot combines an outdoor arts project with a wintertime game. First, fill multiple spray bottles with a mixture of food coloring and water. Allow that water to cool off (you do not want to accelerate snow melt) and then use it to draw a colorful target disc in the snow, preferably in an open area. Now you have a graded target for tossing snowballs at, offering an easy way to determine points.
In this game, a large circle is drawn in the snow with trenches, usually by trudging it out with your own feet and lower legs. The deeper and clearer these trenches are, the better. Then more trenches are plowed to subdivide the circle. The typical design is a pie-like shape, but any design can be used. With the "pie" carved out of the snow, you can now play a winter version of tag. The wintertime-twist on this game is that people can only run in the snow trenches. Anyone who jumps out or falls out of these predetermined paths becomes the new "it."
Wintertime does not always mean a snowy day, especially in some places where snow is a rarity. A winter game that is best played without any snow is the Winter Triathlon, inspired by similar multisport contests at the Winter Olympics. Set up a footrace and a bicycle race in a local park or field, followed by a target-shooting contest with slingshots, Nerf guns, super-soaker water guns or whatever is suitable. Determine a point system before starting, such as five points for first place, three points for second and two points for third, or whatever sounds agreeable. A game such as this one allows kids and adults alike to imagine themselves at the Olympics, and it has the advantage of not being settled in one event. This keeps the attention of the contestants focused for a longer period of time. It also allows a person who is not such a good runner, for example, to shine in another event.