To give the world the benefit of the doubt, "year" could very well be a holdover from some archaic past wherein the seasons followed regular patterns and a year consisted of however many moons, evenly divided between four seasons. I think it's been indicated that this climatic weirdness may be isolated to Westeros itself (which honestly makes even less scientific sense, but I try not to linger on it because it makes my brain hurt),
In that case, maybe a 12-moon lunar calendar was an Andal holdover from Essos, since the Westorosi written records and current institutions started with the Andals. If Westoros had normal seasons sometime between the long winter of the last hero 10,000 years before and more "modern" times I feel like it's a plot hole that Sam or one of the maesters never mention it. The Word of God about Essos having less freaky weather is gibberish though, so the Westerosi climatic weirdness can really be only be chalked up to "a wizard did it".
But to the original question, I don't think you're going to get an answer that satisfies. Their long winters definitely can't be explained by Earth weather, but are measured in something close to our calendar years. At the start of the series Westeros is about to come out of a ten year summer. When they get the raven from the Citadel in the S2 premiere heralding the end of summer, it means fall has started. But winter is coming, fall is only paving its way, and a frighteningly long winter is expected because of the ten year summer. There's no in-plot explanation for how/why a year is the unit of measure for ages regardless of variable season-lengths, it just is. Westoros is part of a fictional world made up by a creator whose expertise is British medieval history and who doesn't display the same understanding or put the same thought into other areas. If Arya Stark's age can only be expressed as 132+ moons, I'm sure the exact count would get away from the author pretty quickly.
Edited by mkwag1015, Aug 31, 2013 @ 7:02 AM.