I want to build a greenhouse accessible only through magic, no outside entrance. Is it possible to have sky and weather on an interior cell? Could I place the greenhouse outside the bounds of vanilla skyrim? Would I need to have a new worldspace? This is something I've not done before and am not sure where to begin. Advice?

If it's just an Interior Cell, then just make one and have a Activator in it that zaps you back and forth to a cell in Skyrim. Easy Peasy. That's all a house interior is, the door zaps you to an interior cell that is supposed to be the interior of the house, but really has no connection to it other than the door activator.

Someone else will have to answer about the weather effects, but it should be possible. I have seen weather patterns in indoor cells in Fallout New Vegas (the weather simulator in one of the DLCs)

As far as the weather goes, if you create a greenhouse as an interior, right click it in the cell view window, there is a Cell Lighting tab in the window that pops up. Look for "Show Sky". It lets you choose a region that determines the appearance of the skybox, you can optionally also check "Use Sky Lighting" to use that region's lighting data as well.