It definitely goes as far south as Brum as my OH says it. I'd never heard it before I met him, though, so maybe it's not used much further south than that.
One lunchtime in my local, on the south coast, a couple - from Derbyshire - came in looking for a light lunch. They asked the barman if the pub did cobs, to which he replied, "What's a cob?" For them, it was a small round loaf or bun, but he had clearly never heard of it, so it may well have spread north, but it seems not to have spread south!
I meant to add above that, in terms of sweat, the rounded idea still applies...ie positive 'beads' of sweat trickling down rather than just general dampness.
Kiki, a cob is a short-legged, stout breed of horse...ie it's pretty 'rounded'!
The word has been used in many contexts where roundness is generally significant, a fruit-stone, a chignon in a woman's hair, a lump of coal and many others...even a testicle!