Well, I was just using fur as an example, since that is known to be a good insulator (which is why animals have it in the first place and people wear furs for warmth, well, maybe not so much today.
Fur is a good example. Insulators are supposed to do just that, keep the cold out and the heat in. Inevitably, all insulators radiate some level of heat above freezing temperature, and snow sitting on it will melt. But fur, being a good example, shows a scenario of how snow can land on clothing without actually coming into contact with the surface of the clothing itself, it will cling to the strands of fur which are more distant to the body. This brings them further away from contact with your body heat, thereby having snow cling to you.
In my experience though (where I have pretty decent winters), snowfall in general will melt on average cotton and wool snow clothing like hats and gloves, but if you get snow on you through some other cause, such as falling into it, getting it thrown at you, or any other such way that makes snow land on you in clumps, then it takes a while to melt. It still does melt, but it clings to you for an extended period of time all the same.
I don't know how it would react to other materials like platemail, but I think in the real world you'd have to be pretty stupid to go out into the cold tundra in a suit of metal armor. Skyrim isn't very realistic in that regard