Like a vacuum bottle that keep liquids hot for a while it's the same inside your boots. Assuming that your vapor barrier isn't perfectly sealed and that there is some heat loss that occurs it is better to keep it on if you stop for a short period of time. But if you stop for too long it's probably better to remove liquids from inside. It will take time to get the heat back on so it is better to change your wet socks that are directly on your feet to get your feet warm again faster and to prevent your cold wet socks to retrieve the little heat that you still have when you have your naked feet directly out in the cold (when your feet is out it is better to be far away from cold wind though or you could get frostbite pretty fast). It takes less time to heat a dry foot that having to heat liquids with it. Liquid act as a 2-way buffer. Takes time to lose heat and time to get it back on. Water retrieve heat faster than air but as long as water stays inside your boots at the same temps than your feet and insulated from outside via the vapor barrier and that you generate enough heat to balance what is lost through insulation it will keep your feet warm. That's why the bunny boots based on this principle are used in arctic.
To get your heat back on faster after having put your naked feet outside in cold air the trick is to push harder for a while to generate more heat to compensate for what has been lost and to wiggle your feet to bring more warm blood.