When have the names been ironic? I don't remember any focus on smithing in Anvil. Windhelm more likely would come from it being windy, and a helm is a helmet. A windmill is something they probably have all over the place, it's a basic tool for grinding wheat and such. I'm not sure why you think Solitude is on an island, I haven't seen any evidence to suggest that. Nonetheless, the entire Northeastern region is snowy. Solitude is right next to the ocean, and also right at the mouth of a river. Windhelm is simply next to a thin river section (it's the size of Oblivion's map roughly, so a river that wide on the map is not very big). Also, if you look, you can see next to the city, some smaller pools of water, which is consistent with the tundra marsh area to the southeast. Although on second look it's possible some of those are light patches of snow, it's hard to tell because it's a bit foggy.