Think "hot press" as in ironing a shirt - resulting in a smooth texture. Cold press is your wrinkled shirt.
I love Hot Press Natural. Excellent blacks. It's my go-to matte paper.
I like Hot Press Bright, as well, but because of its use of OBA's I tend to use it sparingly.
The Cold Press papers are nice, except that the texture is a bit too consistent for my taste. I prefer the more random textures one see's with mould-made papers. That said, Cold Press Natural is a pretty decent proofing paper upstream of the much more expensive Awagami Washi papers.