Look on the hose - you might see the size written on it.
Just out of curiosity, why would someone go through the trouble of installing that when they could easily plug the drain from inside the cooler?
What does the previous owner say about it?
Oh... try taking pics of other sides of the valve - may be some info on it. You may be able to figure it out by measuring the OD with a caliper as black rubber hose, like that, often has the same wall thickness... it doesn't appear to be reinforced hose - just standard stuff. Or back the hose off a bit and measure the barb. Or heck, just remove the whole thing.