Hermesbts will introduce you "holidays korean cares most in 2019". BTS member is korean so i think that you should know before sending letter to BTS. Also it will be a great idea to send letter to BTS at specific holiday for celebrating.
1. New Year's Day (January 1)
As in other countries, the first day of the New Year is celebrated. Many Koreans visit the coast or the mountains to watch the first sunrise of the year.
2. Seollal (February 15-18)
Lunar New Year's Day (Seollal) is one of the most important traditional holidays of the year; the holiday is much more significant than January 1st. Most businesses are closed, and people take several days off from work to visit their hometowns to be with their family. On the day of Seollal, everyone gets up early, puts on their best clothes, and bows to their elders as a reaffirmation of family ties. Feasts are held with specially prepared food such as tteokguk (rice cake soup) and mandu guk (dumpling soup). People play traditional games, fly kites, or spin tops.
3. Chuseok (September 12-14)
Chuseok is one of the year’s most important traditional holidays. It is celebrated on the 15th day of the eighth lunar month. Chuseok is often referred to as Korean Thanksgiving Day. It’s a celebration of the harvest and thanksgiving for the bounty of the earth. Family members come from all over the country for memorial rituals, called charye, at the graves of their ancestors.
4. Christmas (December 25)
Christmas is observed as a national holiday in Korea as in many other countries. To celebrate the festive season, Christmas trees and lights can be seen all over Korea.