Why do different fabrics feel like they are different temperatures?

Note: I’m not talking about their ability to keep you warm, but how they feel to the touch.

Fabrics kept at the same temperature feel cooler or warmer, depending on the type of fabric. A lot of it seems to have something to do with the nap, with higher nap fabrics feeling warmer to the touch than smoother fabrics. (Like sheets, from coolest to warmest: smooth woven cotton> jersey ‘t-shirt’ sheets > flannel > fleece) But, why?

In an example that doesn’t follow that pattern, leather car upholstery feels much warmer or much colder than other fabric seats, depending on the outside temperature. Why is that? Maybe leather isn’t really considered a fabric?

Another odd example: If I take off a pair of regular socks (which should presumably be at body temperature), and put on a pair of ‘fuzzy’ socks (which were in a drawer and should be at room temperature), my feet instantly feel warmer. What’s up with that?