I'm looking for the word that describes snow mixed with rain.
I looked up the dictionary.
It says `sleet`, but I think I've heard the word that starts from 'F'.
Is there any word?
You might be thinking of 'frost' however, frost has a different meaning:

Frost - A deposit of minute ice crystals formed when water vapor condenses at a temperature below freezing.

Sleet - A mixture of rain and snow or hail.
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Is there a word to express a mixture of love and hate?
mix. of snow and rain: flurries