Why does Japan get so much snow?
From my understanding, you are thinking along the right lines but also need to take mountains into account.
Ireland's mountains are lower than Japans. I think that Japan's mountains are a similar height to Oregon's but the high mountains are closer to the coast in Japan. (I don't know either area well, so this statement could be wrong.)
Another thing to consider is that in winter, convective showers are common over the sea. A longer sea track will have more showers and therefore more mixing of the atmosphere, raising the temperature of the air mass.
Winter convection cuts off over land, but showers can penetrate inland a little with the momentum they already have. The closeness of the mountains to the coast in Japan, as well as their height, will give more orographic enhancement to the amount of precipitation as well as possibly reinvigorating the unstable convection by forcing it to rise. Ireland's lower lying status won't have this effect as much.
Oregon has two ranges of mountains, the lower Coastal Range (&lt;1000m) and the higher but 150km inland Cascades (~3000m). The Coastal Range has a similar height to the Irish mountains but are longer in their extent. The orographic enhancement of the Coastal Range will be much less than in Japan. The Cascades will then be in a rain shadow as the air will be less humid downwind of the Coastal Range. While the Cascades still cause orographic enhancement, this is nowhere near as much as if the Cascades were by the coast, which in Japan they effectively are. You can see this effect on the annual average precipitation map of Oregon:

As an aside, I had wondered if the Sea of Japan might be warmer than around Oregon and Ireland; this would provide more heat, moisture and instability to the air reaching Japan. I had a quick look at February sea surface temperatures, and they seem broadly comparable to the other areas, at least for the past three years, so this enhancement mechanism seems unlikely. February appears to be the month that Japan gets the most snow, although I'm not sure if that's talking about peak snowfall or peak accumulation.
I found a few articles about Japan's snow online:

National Geographic: The world's snowiest place is starting to melt
Ski.com: Why is there so much snow in Japan?