Yes, according to all English title capitalization rules, you must capitalize the holiday title. This includes both holidays where businesses are closed as well as church holidays.
If the holiday contains multiple words, all words should be capitalized in the title. For example: New Year’s Day.
Even if the holiday is shortened, such as in “New Year’s,” both words should still be capitalized.
A list of the most common holidays capitalized is below:
Advent
All Saints’ Day
Australia Day
Bastille Day
Boxing Day
Canada Day
Christmas (also Christmas Day and Christmas Eve)
Coming of Age Day (Japan)
Easter
Epiphany
Father’s Day
Good Friday
Halloween
Hanukkah
Holocaust Remembrance Day
Holy Thursday, Holy Saturday, Holy Week
Independence Day (US) also the Fourth of July and July Fourth
Kwanzaa
Labor Day (US)
Labour Day (Canada and other nations)
Lent
Martin Luther King Jr. Day (US)
Maundy Thursday
May Day
Memorial Day
Michaelmas (the feast of Saint Michael the Archangel)
Mother’s Day
New Year’s (also New Year’s Day and New Year’s Eve)
Passover
Presidents’ Day
Purim
Ramadan
Remembrance Day
Rosh Hashanah
St George’s Day (no period or full stop with St in BrE)
St. Patrick’s Day (also Saint or St Patrick’s Day)
Thanksgiving (also Thanksgiving Day)
the High Holy Days
Twelfth Night
Valentine’s Day
Veterans Day (no apostrophe)
Victoria Day (Canada)
Victory Day (Russia)
Yom Kippur
