It is Happy Holidays, with both words capitalized. "Holidays" is pluralized because (generally) you are referring to more than one day of the holiday.
The correct saying is "Happy Holidays", now you know
If you are referring to one holiday: Happy Holiday If you are referring to more than one, such as Christmas and New Years: Happy Holidays.
happy holidays
Happy holiday and Happy holidays mean two different things, but both are correct.
merry christmas, and any other holidays