When the water is warmer than the air, especially if the air is pretty still, you can definitely get funky water-hugging fog effects. One thing you have to know about water is that water is always evaporating. Even ice is always evaporating (slowly, and technically mostly it's sublimating), no matter how cold it is. Water molecules don't hang onto each other super-tightly, which is why it's a liquid at room temperature.
Water's always causing humidity, if you want to think about it that way. And the colder the air is, the less moisture it can absorb. The more humid the air already is, the less moisture it can absorb. So if the air can't hold anymore water, and there's no wind, you can get fog sitting its ass on the water in weird ways. I guess it might technically be mist rather than fog; I'm not sure about the rules there.
In Vermont, we had a lot of really cold mornings where there would be a zillion distinct little columns of mist rising up off the river, maybe two to five feet high. The upper boundary was always a flat plane -- there was a ceiling beyond which the mist evaporated. The columns are a little wavy and maybe a foot away from each other. It's pretty trippy. The river was very slow in the middle of the winter, with no thawing going on, and the effect was pretty phenomenal behind the dam, where the river was fat and especially lazy.
