Move along slippery surface with girl following cones maybe (3-5)

I believe the answer is:

ice-skate

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'move along slippery surface' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'girl following cones maybe' is the wordplay.
'girl' becomes 'Kate' (girl's name).
'following' means one lot of letters go next to another.
'cones maybe' becomes 'ices' (I can't explain this - if you can you should believe this answer much more).
'kate' after 'ices' is 'ICE-SKATE'.

'with' acts as a link.

Can you help me to learn more?

(Another definition for ice-skate that I've seen is " travel in winter".)

I've seen this clue in The Times.

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