Nose bleeds are pretty common during the winter months since the air in winter is dry and that dry air causes your blood vessels in your nose to break and bleed.
The blood vessels in your nose are very tiny and can crack easily due to drying out.
Also when the furnace is on or the heat is on the heater drys out your air inside your house so it's a good idea to use a humidifier in your home to add moisture to the air to help with the dry out and prevent your nose from bleeding.
The humidifier will also make the home feel warmer and prevent sore throats as well.