Hi Eamon,
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.