According to “Shmirath Shabbath K’Hilchata” (R’ Yehoshua Neuwirth)
English Vol. 1 p.197, “It is not permitted to make snowballs or a snowman, but the snow itself is not muktzeh, even if it fell on Shabbath or Yom Tov.”
p.174 (paraphrase) – snow may be shaken off clothing but only gently, unless the material is made from non-woven plastic sheets, when it can be done even vigorously.
But of course consult your Rov. As for children, I guess it depends on what you consider the age of chinuch, same aa for playing with a muktzeh toy on Shabbos.