I succumbed to hypothermia during a long winter hike several years ago. Initially, I was freezing and shivering - it gets to the point where you feel as though your teeth are smashing together with such violent force that they're going to break and fall out. That for me was the most unpleasant phase. The next thing I knew and I'd started to warm up, I assumed it was because we'd moved to an area of hotter air or got out of the wind or something but this was the hypothermia progressing. I felt quite pleasant actually.
Next thing I knew, I was too hot. I don't think I was sweating but I felt like I was. I loosened my outerwear and took off my thermal hat, it was at this point that my hiking buddies noticed what was going on and intervened. So I don't have any practical experience to share beyond that, but beyond the initial stage of actually feeling the cold and violent shivering, it was quite pleasant.