We don't know of the Mando'a names of any special Mandalorian holidays, though we do have some information about the kinds of things that Mandalorians typically celebrate; check this post for details: Holidays.
Fans have come up with ways to express in Mando'a various Earth holidays.
Briikase gote'tuur: Happy birthday.
Briikase vutyc tuure: Happy special days. Happy Holidays.
(or just briikase vutyc tuur when talking about one day)
Briikase vutuure: Happy Holidays.
(Uses a MandoCreator/Oyu'baat word.)
Ca be chaab: Night of fear. Halloween.
Oyayc'tuur: Life day.
(This is pronounced the same way as oyacy tuur, alive day, though since that phrase doesn't make sense, I doubt there would be confusion as to what it referred to. Promoted in 2020 by Albertamanda on Tiktok. Since "life" is spelled oya'cye/oyacye — different spellings in the same article — it should technically be Oyacy'tuur.)
tuur par cyar'ikase: day for sweethearts. Valentine's Day.
tuur par burc'yase: day for friends. Sweetest Day/Friendship Day.
tuur par buire: day for parents. Mother's Day/Father's Day/Parent's Day.
tuur par ba'buire: day for grandparents. Grandparent's Day.
tuur par gedeteyar: day for being thankful. Thanksgiving.
(Mentioned in the Mando'a Lessons Discord server.)
evaar'la simir: new year.
ude'tuur: rest day.
(Mentioned in the Mando'a Lessons Discord server.)
aayhan'tuur: memorial day (generic term).
(Mentioned in the Mando'a Lessons Discord server.)
Note that Life Day is "officially" celebrated on Earth on November 17, because that is the anniversary of the premier of the Star Wars Holiday Special. Nonetheless, it doesn't seem that most people know that, so use it as a replacement for "Christmas.