Is it permissible to cross country ski on Shabbat if there is an Eruv?
I can't see the reasons to prohibit skiing different to the reasons to prohibit bike riding (which is accepted by all): 1. Uvdin DeChol – weekday activity that doesn't meet the spirit of Shabbat. 2. One might exit the borders of Shabbat accidentally. 3. If brakes, one will be tempted to fix it. (See also Tzitz Eliezer 7; 30)