Few people know the definitions of a carol. There are several, and you must define what kind you are talking about. Following from OED, the standard of the English language. I have skipped over some sub-headings.

I ring dance
1. A ring dance and derived senses.
   c. A company of dancers or singers, a choir.
2. To sing, originally that to which they danced, but now to sing a lively and joyous strain. (Rudolph, Here Comes Santa, Jingle Bell Rock, etc.)
3. a. A song or hymn of religious joy.
   b. Especially: a song or hymn of joy sung at Christmas in celebration of the nativity. Rarely, applied to hymns sung on other festive occasions.

Shhh! Unhappy carols are not mentioned.

II. A ring and related senses.
4. A ring or circle, e. g., of standing stones.
5. A small enclosure, or 'study' in a cloister.
6. a chain (Middle Ages, not sure I understand the examples).
7. Combined; carolsynge, carol-chanting, carol-wise, etc.

Carol- the verb. ------