Cob is an old word meaning something round. It also was used to describe a spider - as in cobweb. My suggestion for the above phrase is that when one is sweating profusely the beads of sweat feel like a spider scuttling down one's face, or alternatively the feeling of walking into a spiders web.
Yes it was used in Birmingham in the sixties. I used it myself. Not heard it for a long time.
Apparently, sweating like a hooded, is occasionally used by certain people.
I never realised that everyone didn't say it, I think the reason I've never found Peter Kay funny is because so much of what he says is quite normal to me, being Notlob-born! A cob is a small horse so I assumed that was the origin of sweating cobs.