Unilateral headache may be due to migraine, ear, sinus or jaw infections, temporal arteritis. Pain on one side of the head, in an elderly patient, brought about or increased by cold and during night times can well be temporal arteritis. Other signs like anemia, fever and high ESR, weight loss, sweats also may be seen. This may be accompanied by pain in the neck, back. If your mother has any of the other symptoms, you must immediately consult your GP and ask to be investigated.
Thanks for writing to the forum!
There are two main things she should look at. Consult an ENT for an internal ear infection. The other possibility is temporal arteritis.
It could also be migraine. However it could also be a migraine triggered by cold weather. Just covering the head will not help as the sinus can be exposed to cold air though the nostrils. Avoiding the cold weather and staying indoors is the best treatment.
Please let me know if there is any thing else and do keep me posted. Take care!