The monster under the bed can’t get you if :

1. You’re feet are covered.
2. You’re head is covered. I thought this was common knowledge.

Conversely, I like to have my feet poke out from under my duvet.

This is due to vasodilation.

"Vasodilation occurs in superficial blood vessels of warm-blooded animals when their ambient environment is hot; this process diverts the flow of heated blood to the skin of the animal, where heat can be more easily released to the environment. The opposite physiological process is vasoconstriction. These processes are naturally modulated by local paracrine agents from endothelial cells (e.g., nitric oxide, bradykinin, potassium ions, and adenosine), and by the autonomic nervous system and the adrenal glands, both of which secrete catecholamines, such as norepinephrine and epinephrine, respectively.[6][7]"

It's the opposite of vasoconstriction, which occurs when you're cold and your extremities have less blood flow to prioritize the warmth of your core organs.

For the same reason that orgasms are better if you're wearing socks.

Sounds like circulation issues, exercise, Diet, and blood pressure will have a impact on how well your extremeties get blood and feel "cold"

Feet don't have a lot of fat for insulation so they tend to rely on the circulation system to keep warm. Just like your hands.