Arrid extra dry cream (with aluminum chlorhydrate!). The spray goes everywhere and smells up the whole locker room so use the cream or maybe roll-on. It really works to keep your feet dry which usually means feet can be warm in your boot. You don't need to put it on every day. Once a week might be enough, I use it even less often because we only get an occasion cold snap around here. I don't know how it stops the sweat. I have not experienced any negative side effects. I keep it off my toenails so they don't dry out, but it probably doesn't harm toenails, I think it's safe.
For hands, it might not be effective, because the part that gets cold (fingers) is a lot farther from the part that sweats (palm). I have gloves with liners that keep my hands warm. Chemical hand warmers, gloves with pouch for handwarmers, mittens might help with hands.
My hands don't get cold when I ski because they are conditioned to the cold. I ride my bike with fingerless gloves whenever possible.