Just to continue poking this bear with a stick...
There is no, repeat, no grammatical reasoning involved in the choice between "Season's" and "Seasons'". Both options are perfectly grammatically correct.
Asking "grammar experts" to solve this issue is pointless. Graduates of every fifth grade term should be able to decipher the inference of this fluttering apostrophe. Is it one, or is it many?
This is an issue of intent, and Thadeus, if you intend to wish the MacMurtry-Surfensteins happiness in any and all seasons they wish to enjoy, then by all means wish them "Seasons' Greetings".
I don't want Thadeus and his lot going wild, celebrating seasons willy-nilly, driving their pagan motorbikes on my lawn, so I greet them for one season at a time. At least I allow a choice of which season to accept my greeting for.
Why the deuce does anyone give a flying rat's butt whether I greet them seasonally anyway? I'm not clear exactly what a "season's greeting" would entail anyway... Welcome to Summer, fine friend! Hale fellow, shall we away into the Spring? Enter into Autumn with me, that we may enjoy the harvest bounty!
I'm not sending cards this year.
[red]Note:[/red] [gray]The above comments are the opinionated ravings of Mr3Putt. As such, Mr3Putt accepts no responsibility for damages, real or contrived, resulting from acceptance of his opinions as fact.[/gray]