Probably not. Cold feet at night is a very, very common complaint. That cold feeling generally has nothing to do with your circulation, which is almost always normal in these circumstances. If you are really worried, see your doctor but most of the time, all you need to do is wear socks as dr. Salartash suggested.
Wear socks. Nothing to worry about. Wear socks.
Circulation. Typically the reason your extremities are cold is due to poor circulation, it's a common thing and usually affect the lower extremities due to the further distance from the heart, your feet will feel colder at night because naturally your heart rate lowers at a state of rest, vitamin c and co q 10 helps improve circulation.