The saying sweating like a pig actually refers to the pig iron melting process.
When pig iron is made the iron goes through a smelting process in which hot iron is poured on sand and cools and solidifies with the pieces resembling a sow and piglets.
This is where it gets it's name pig iron and the term and saying sweating like a pig comes from the hot pig iron and the people who work in iron smelting facilities would sweat.
So while pigs cannot sweat the saying doesn't actually come from pigs but instead the saying comes from working with pig iron that makes you sweat.
It gets really hot in an iron smelting factory which means you would sweat.
I used to wonder why we said sweating like a pig when pigs did not sweat and I asked my Grandpa that before as a kid and he said it was because of the pig iron and not the pig.
My Grandpa used to work in an iron smelting factory.