I have perfectly ordinary standard-pull brake levers on my bike. When the temperature gets below 20F or so, the left-hand one seizes up, not wanting to pull, and not braking well if I force it. Once the temperature warms up a bit, it's fine.
Diagnosis? Cure? I'm pretty sure the actual brakes are fine, and the cable looks okay too.
(If there's a duplicate, feel free to kill this one; I looked but didn't find an exact symptom match.)