The most common and most likely answer to this crossword clue is the 4 letter word RIME
I've seen this crossword clue in The Guardian
R
I
M
E
Buddy explains!

The straight part
We know that "Frost" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case frost = rime.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 RIME mean?
RIME noun- Ice formed by the rapid freezing of cold water droplets of fog on to a cold surface.
- A coating or sheet of ice so formed.
- A film or slimy coating.
- To freeze or congeal into hoarfrost.
- To compose or treat in verse; versify.
- (followed by with) Of a word, to be pronounced identically with another from the vowel in its stressed syllable to the end.
- Of two or more words, to be pronounced identically from the vowel in the stressed syllable of each to the end of each.
- To number; count; reckon.
- Number.
- Rhyme.
- The second part of a syllable, from the vowel on, as opposed to the onset.
- A step of a ladder; a rung.
- A rent or long aperture; a chink; a fissure; a crack.