This is an excerpt from Teaching Cross-Country Skiing.
Fox and Geese
Large, brightly colored fabric squares or short swim noodles for taggers to carry; a large circle to ski in that is divided into six or eight wedges
In this tag game, skiers (geese) must ski in the existing tracks as they move around the circle attempting to avoid being tagged by the It (fox). See figure 5.1 for the setup. Select several skiers to be foxes and identify them with either swim noodles or brightly colored fabric squares. The center of the circle is the safety zone (goose nest); one skier at a time can ski into this zone and stand until another skier wants to come in. The first skier must then leave. The last skier to be tagged becomes the next fox. No poles are used. This game can be played with skiers wearing both skis or just one ski.
Frisbee, cones to mark bases
This game is baseball played with a Frisbee and on skis! To start the game, the at-bat skier throws the Frisbee as far as she can and then skis off to first base. A caught Frisbee on the fly is an out. To tag a skier out, another skier holding the Frisbee must tag the skier. A run is scored when the skier makes it safely around the bases. No poles are used.
Cones to mark playing area
In this tag game, one person is “The Germ” who tries to tag other skiers moving around the playing area. When “The Germ” tags another skier, the body part tagged is rendered useless. For example, if a leg is touched by “The Germ,” that skier must ski on one ski. Skiers may be tagged more than once. If skiers run out of forearms, shoulders, legs, and equipment, they run in place until another skier frees them by tagging them.
Read more from Teaching Cross-Country Skiing By Bridget Duoos and Anne Rykken.