Plants need light and good ventilation to survive. A closed shed with no windows would cause the plants to suffer. Do you have a conservatory or front porch to the house? This would offer better protection.
During the course of a 'nomal' winter we only get a few days and nights when it is really cold, the rest of the time it is usually just dull and damp. You could keep the plants outside for most of the time, keep a close eye on the weather forcast and bring them into the shed for the short period of really cold weather.Then bring them back out again asap. If there are not many plants you could stand the pots just inside the shed and leave the door wide open for most of the time, just closing it when the weather demands.
The compost in the pots should be kept 'just moist' during this time. It is better to be too dry than too wet and just give a little water at a time. Try not to water immediately before a freeze-up, the plants would rather be cold and dry than cold and wet!