Schooled with disregard for cold in Oxford? (4)

I believe the answer is:

shoe

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'oxford?' is the definition.
(oxford is a kind of shoe)

I can't explain the rest of the clue.

(Other definitions for shoe that I've seen before include "What's worn" , "Foot-covering" , "Hose (anag)" , "Oxford, say" , "Card dispenser" .)

I've seen this clue in The Independent.

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