Hi Joseph, I'm sorry you didn't get a response earlier.
Your idea comes up fairly frequently in
beekeeping circles and, while I haven't tried it personally, those who have invariably seem to give it up. First of all it is based on a major misapprehension about what bees are doing in winter.
Winter bees are biologically quite different from summer bees. The winter bees are fed additional food as larvae to build up their fat reserves which helps them live a lot longer than a normal forager bee in summer. Their "job" is to survive the winter expending as little
energy as possible, by clustering in the hive for warmth. When there is an occasional warm spell they break cluster and fly briefly to defecate outside of the hive. They live off the reserves of honey in the hive, not foraged nectar.
Well adapted bees can cope with the cold very well - especially if their box is well insulated (for example a polyhive - wrapping hives is making up for a fundamental shortcoming in traditional thin-skinned wooden hives).
What they struggle with is periods of warm weather, followed by a further chill. The warm wakes them from torpor and sets them flying. If it is very warm they might even start trying to raise brood and forage. This increases their consumption of stored food considerably compared to a prolonged cold spell. When the cold returns the brood they tried to rear is chilled and dies (sometimes) and the life of the bees is considerably shortened.
Your
greenhouse proposal is essentially trying to trick the bees into ignoring the cold weather and remain flying all year. This is quite unnatural for the bees, and the ones adapted to your cold winters will not cope well. Additionally you will not be able to provide adequate forage for them in a green house, so they will either head outside and freeze, or you will need to continually provide sugar water for them to forage.
Overall it is best to stick with what the bees do in nature. If you want to help them along make sure they have super-insulated hives.
