It is actually fairly common to have nose bleeds occur at night. Most of the time, this is because the dry air in the bedroom while you are sleeping (which is made worse in the winter, due to heating of the room). The dry air leads to drying out of the nasal lining, which leads to cracking and bleeding
One solution to this problem is either to turn down the heat in the bedroom, or to consider using an air humidifier while you are sleeping. In addition it would be helpful to talk with your primary care doctor
about the problem, because there is often an underlying condition that contributes to the irritation and dryness of the nasal passages that can be corrected.
For example, nose bleeds are more likely to occur in those who suffer from chronic nasal allergies or sinus congestion. If you adequately treat the nasal allergies or sinus congestion, which can be accomplished with a combination of very effective medications prescribed by your primary care doctor, then the inflammation will be reduced, making you less predisposed to nose bleeds.
Your doctor will be able to examine your nose and throat and determine if you have allergies and, if so, prescribe the necessary medications.