The most common and most likely answer to this crossword clue is the 10 letter word SNOWBALLED
I've seen this crossword clue in The Times
S
N
O
W
B
A
L
L
E
D
Buddy explains!
The straight part
We know that "Went ballooning" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went ballooning = snowballed.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SNOWBALLED mean?
SNOWBALLED verb- To rapidly grow out of proportion or control.
- To play at throwing snowballs.
- To pelt with snowballs; to throw snowballs at.
- (sexual slang) To receive a man's ejaculate in one's mouth, and then to pass it back and forth between one's mouth and his.