Similar to the concept of storing clothes in your sleeping bag overnight to keep them warm, sleeping with your boot liners in your bag can give your feet a boost in warmth even if your boots are frozen stiff.
If your boots have removable liners, simply remove them from your boots and sleep with them in your sleeping bag. You'll want to be sure your boot liners are dry before sticking them in your sleeping bag. Have a tendency to get cold feet? Sleep with the boot liners on your feet for extra warmth. If your feet have a tendency to sweat, don't wear the boot liners in your sleeping bag. Beginning a cold day with damp boots will start you off on the wrong foot.
In the morning your feet will be a little warmer when you slip that toasty liner into your boot, which will help make activities like starting a fire and taking down your tent easier on your extremities.