Get tested for sleep apnea.
Antihistamine. Benadryl works wonders.
You may be breathing through your mouth, not your nose. You won’t know, because you are asleep.
You could wear a winter facemask or wrap a scarf over your nose and mouth.
If you have sleep apnea and health insurance, you might be able to get a cpap machine with a humidifier
You might try making a tent over your bed. Blankets suspended over your bed to trap warm air and protect you from drafts.
Dome tent would work. 30 dollar kids fort type from Ikea.
Are you able to plug in a humidifier?
I use a Mr Buddy propane and it adds comfortable humidity to the dry cold.
Source: Seeking advice – every time I sleep in cold, I wake up with heavily sore throat from breezing with my nose. How do you deal with that while camping in cold eviroments? Have no problem with cold other than this one.