According to the dictionary, Weihnachten is neuter, yet the "fröhliche" variant seems to be widely used. That does not happen eg with "gutes Neues Jahr", which is as expected since Jahr is neuter.
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I will also throw in my opinion on this.
As you know, compound nouns (generally) adapt the gender of the last compound part.
is correct then. The funny part comes now. "Weihnachten" (n) is actually the substantivated progressive form of "Weihnacht".
When substantivating verbs, we can in general assume the neuter gender:
correctly declined this is then:
This means, up to now, grammatically correct would be:
But Weihnachten also is an old plural form in the old German Mittelhochdeutsch, as seen in this post. Thereof we can conclude there also exists
and that leads to the grammatical correctness of
I'm most familiar with
(in parts due to this Christmas carol) and
are both used as well. The former would technically be incorrect (or possibly plural), but is probably the more common one of the two - in particular, I think I've never seen the latter in print.
There are regional differences involved, though, so your mileage may vary...
feels wrong to me, whereas
don't, which agrees with c.p.'s Wiktionary link that has feminine die Weihnacht, neutral das Weihnachten and plural die Weihnachten.
One finds the explanation in the first line of the Wiktionary entry for this word.
Weihnacht (feminine noun) and Weihnachten (neuter) are then different words. If you find fröhliche Weihnachten, it must be the plural.
By the way, slightly off-topic: Does one say an or zu Weihnachten?
The answer is here, taken from one of my favourite sources (Atlas zur deutschen Alltagssprache):
Yes. The simple answer is, it's plural. Weihnachten = geweihte Nächte = holy nights.