(1) Wish you a Merry Christmas!
(2) Wishing you a Merry Christmas!
They are both correct and there's no real semantic difference between the two, though it does depend on context. I would have thought that (2) was heard more often than (1), but the graph says otherwise: https://books.google.com/ngrams/graph?content=wish+you+a+merry+Christmas%2Cwishing+you+a+merry+Christmas&year_start=1800&year_end=2008&corpus=18&smoothing=3&share=&direct_url=t1%3B%2Cwish%20you%20a%20merry%20Christmas%3B%2Cc0%3B.t1%3B%2Cwishing%20you%20a%20merry%20Christmas%3B%2Cc0
(1) is a 'subjectless clause', so-called because the subject has been ellipted (omitted), cf. I wish you a merry Christmas.
(2) is a gerund-participial clause, typically used as an adjunct, cf. Wishing you a merry Christmas, I'll see you in the New Year.
Thank you, Paul! I've got it!