I have mountain horse paddock style boots and they are so warm. I got them last winter and they've held up nicely. I know all about bad circulation, I have reynauds disease so it's really hard for me to do anything outside in the winter and still be able to use my hands and my feet get pretty bad too. I go for two pairs of socks and these boots I have, they mostly do the trick.
I've yet to find anything that helps my hands so that's what usually dictates if I ride or not.
As for your hands, my doctor told me a while ago to get Arctic gloves/mittens. He said army surplus stores online tend to have them. They're a bit pricy, but probably worth it.