To sweat like a pig

Since pigs dont have sweatglands, I have often wondered why we use the expression "to sweat like a pig" or in Norwegian; "Å svette som en gris".
I have not been able to get any closer to the origin of this expression, but at least I have been able to confirm my suspicion that this has somehow been started by one of the other farm animals (possibly the "cute" sheep?) to somehow heighten their own worth by lowering that of the pig?
The excerpt below is in Norwegian and can be found in the link below, but the main gist is as follows:
Because the pigs cant sweat they roll around in mud to cool down. The process of vaporizing the water in the mud requires energy and thus reduces the temperature for the pig. It's basically the same as we do, but we dont need mud in order to do it.
So why mud you might ask yourself - well mud cools/vaporizes more slowly than water; thus prolonging the cooling process for the pig.
So we might in fact say "clever as a pig" from now on.

The next qustion is whether the pig mafia of the east has anything to do with the spreading of the expression "dumb as a sheep". All the pigs in question refused to comment.

Når vi mennesker blir litt varme i trøya begynner vi å svette, men å si at man svetter som en gris er ikke bare en fornærmelse for svinet, men i tillegg en blank løgn. Griser svetter nemlig ikke i det hele tatt, og det betyr at de ikke har noen innebygd måte å kvitte seg med varme på. Men svin er ikke tapt bak noen vogn må du tro! I stedet for å gjøre huden våt med svette, ruller de seg på fuktig mark og blir våte likevel. Idet fuktigheten fordamper stjeler vannpartiklene energi fra huden, og grisen blir kvitt den overflødige varmen.

Det er heller ikke noen tilfeldighet at svina velger å velte seg i gjørme. Vannet i mudderet fordamper nemlig saktere enn rent vann, og dermed får grisen en passelig langtidskjøling i stedet for superkjapp pangkjøling

http://www.nrk.no/programmer/tv/newton/1653766.html