Sorry, but this question, �Which is correct, Season's Greetings or Seasons' Greetings�, is one pedant�s (or many pedants�) dream. So please, don't be running off with the toys just yet . . .
As sophieb so correctly pointed out, this part of the year, encompassing Christmas, (or X-mas if you prefer), New Years�, Winter Solstice and possibly inclusive of Thanksgiving, is collectively one season. Therefore, �Season�s Greetings� is grammatically correct . . . but either way, Ill� no't be' refusin'g any' gift's you' sen'd t'his 'way!