Assume that there is an eruv between one's home and shul. Can one cross country ski to shul on Shabbat? Possible concerns:
Making marks (tracks) in the snow with the skis and poles. Is this any melacha that may be prohibited?
Related to this M.Y. question - This is strenuous exercise that is not for refu'ah and it is not for the purpose of enjoyment. (Assume that the person generally likes X-country skiing, but since there is heavy snow, he'd rather be home if he could. It's that he's the Torah reader, so he has to get to shul.)