I Googled it:
Being either afraid of the cold or feeling the cold a lot. Used across the Midlands of England and the north.
........"You nesh git, you don't need a coat."
Averse to cold weather; soft, delicate'* 1913:
.........."F-ff-f!" he went, pretending to shudder with cold.
"Goodness, man, don't be such a kid!" said Mrs. Morel. "It's NOT cold."
"Thee strip thysen stark nak'd to wesh thy flesh i' that scullery," said the miner, as he rubbed his hair; "nowt b'r a ice-'ouse!"
"And I shouldn't make that fuss," replied his wife.
"No, tha'd drop down stiff, as dead as a door-knob, wi' thy nesh sides."
— DH Lawrence, Sons and Lovers
(Bit of a pompous speech that last one - but that's DH Lawrence for you. On second thoughts 'self-conscious' would be better) Wikepedia will probably tell you as much about 'nesh' as you need to know.
Anyway, today's been a day for feeling nesh. It's cold. Damned cold. Any daffodil thinking of flowering prematurely should think again.