Short version: cold and humid weather are the enemy of a good finish, so don't push your luck.
Most manufacturers — Farrow & Ball, Little Greene, Dulux, Benjamin Moore — quote a minimum application temperature of around 10°C, and that's surface temperature, not just air temperature. A north wall in January can be several degrees colder than the room reads, so check the wall itself. Below 10°C, water-based emulsions and acrylic eggshells won't coalesce properly: the film never knits together, and you end up with a weak, patchy, easily-marked finish. Oil-based paints get gloopy and dry painfully slowly.
Humidity is the bigger trap, because it's less obvious. Above roughly 85% relative humidity, the water in the paint simply can't evaporate, so drying and recoat times stretch out massively. On trim and woodwork this is where you get that horrible tacky, never-quite-hard feel that picks up dust and fingerprints for days. Bathrooms and utility rooms are common culprits — paint when it's been ventilated and dry, not straight after a shower.
My practical rule: aim for 12–22°C and decent airflow. Crack a window for ventilation but don't blast cold draughts straight onto wet paint. In winter, warm the room a few hours before you start so the walls themselves are up to temperature, and don't paint late afternoon when temperatures are dropping — you want it touch-dry before the evening chill.
If you're doing exterior work, Sandtex masonry and exterior ranges from Little Greene and Dulux all need a dry spell with no rain forecast for at least 4–6 hours after, ideally longer. Never paint exterior surfaces in the morning if there's been overnight dew or frost on them.
For a forgiving winter interior job, Earthborn's claypaint and breathable emulsions cope well with slightly damp old plaster, and a warm, easy colour like Setting Plaster or Slipper Satin hides minor application quirks better than a flat cool grey. Get the conditions right and the paint does the work for you.