The simplest option is not to use 'wish' with 'season's greetings' ! Think about it: how do you 'wish' greetings? You may wish someone a happy Christmas or a happy holiday. You can't wish them Christmas, only that the Christmas is a happy one. You may 'send greetings' but 'wish greetings'? No.
The simplest way, if you want to use 'greetings' as your word is to put 'Season's greetings!' at the end of your letter.Or you could put "we send you Season's greetings"
"Would to" is never grammatically correct. " Would wish" is itself clumsy. Either you wish or you don't. "Would wish" sounds either conditional or repetitive. You either do wish or you don't wish. You don't 'wish to wish' or 'want to wish' or wish if the circumstances permit, if you get the opportunity to wish.