Our house temperature drops to 3oC during winter when our newborn is due. Is there any kind of safe heater we could get for our room while baby is in there over night, even on low. I have concerns about their face and head at temperatures that low?

Red Nose does not recommend that a heater is necessary in baby’s sleep room.
However, if you do have a heater on when baby is sleeping the following guidelines from safety & government organizations as well as Red Nose are important to prevent accidents &/or overheating.

Ensure heater (& any cords) is out of baby’s reach
Have a window slightly open to allow for fresh air circulation.
It is a good idea to use a heater with a thermostat to prevent room from becoming too hot, as this may lead to overheating.
Ensure baby’s head & face remain uncovered.
Dress baby according to room temperature, not the outside temperature.

Also, have a look at this information:
https://rednose.org.au/article/what-is-a-safe-room-temperature-for-sleeping-baby