Way back when, I got a pair of Zero-brand mittens that are the warmest I've owned. They're also waterproof. They're also water vapor proof. That means they make my hands sweat. And after doing a fair bit of hiking and snowshoeing in Colorado, I really only used them a very few times. I had some regular wool mittens that worked better for general snowshoeing. Bicycling introduces more wind and would make those somewhat less useful. I definitely would vote for mittens, though, which are underappreciated.
I remember seeing mukluks in a surplus store. Careful with some of that stuff. If it gets cold enough, snow falling on you, or being walked through, doesn't melt, and you don't really need waterproof stuff. So stuff that might work great in Antarctica isn't necessarily the right thing in a cold wet climate.