most high end mx boots have hinged ankles, and allow easy walking. several mx/adventure boots are gore-tex lined, and or waterproof. are they warm, depends on activity level. heated insoles will help too.
using your above scenario, you wont make it very far in stiff snowboard boots. the whole idea is to get a compromise, enough protection to avoid injury to your feet, or ankles, and enough dryness, warmth to get you through the day.
on the protection thing... you take a bad footpeg landing with a front toe tip, in sled boots, prepare to taco your foot, and spend the next several months rehabbing it. same with ankle twists ect... buy as much protection as you can afford. Ski