Why are carols associated with Christmas?

Answer 1

The word Carol actually means dance or a song of praise and joy! Carols were part of year round Pagan rituals that were "Christianized" in the 15th century.

The earliest Carols told the story of the Nativity as an occasion for rejoicing.

Answer 2

because they are Christmas carols and people sing them only on Christmas Day!

More detail:

Christmas carols are sung and played throughout the Christmas season to celebrate the birth of Jesus, and to celebrate the holiday season. Many of the carols are very spiritual, while others are more 'fun and upbeat'. But all of them are to celebrate Christmas - the birth of Christ.

Perhaps they should not be considered as Christmas carols but their are a number of purely secular songs that are heard only during the Christas season, such as Winter Wonderland, Frosty the Snowman, Jingle Bells, Silver Bells,Chestnuts roasting on an open fire, Let it snow, etc.