Did you mean Christians? Because there is no Satan (as such) in Judaism. Specifically the 'adversary' is more like a prosecutor and has not fallen (and because free will is not something angels have in Judaism, could not fall).However. When the followers of the Judaistic religions came in they took the image of the Horned God and declared it as Satan.
As for Christmas, the traditions associated with summer and winter solstice is unique to no pagan society and is commonplace to all agrarian cultures. For example you'll find ancient winter tree decorations everywhere from Scandanavia to Rome to Japan. And while Germanic pagan celebrations undoubtedly influenced the culture of Christians (and visa versa) calling it stealing is pretty hyperbolic. Does that mean Germanic winter celebratons were stolen from earlier Egyptian ones? Ironically the birth of Horus was, like Jesus, originally celebrated in the summer but moved to the winter because
A. Winters are boring in agrarian society as there is little to do but wait for spring field work and calfing animals, so it's a perfect holiday time.
B. Fits symbolically with gods delivering people from darkness.
C. End of winter is observed world wide as a time of new beginnings, with big feasts and gift giving.