The greenhouse was originally Anthy's. I don't think anyone built it; I think it just appeared one day, back when the outdoors was nebulously transitioning between being an exact replica of the Hogwarts grounds to being the psychosomatic geography we all know and love. My memories of this are equally nebulous, though, so I could be forgetting something. She grew lots of roses in there, but various other people had bits of it; I'm pretty certain Elaine had some lilies and such there from early on.

When Anthy finished her canon she moved all her plants out of it. Meg got killed there. (Oops.) Somewhere in there Mary Lennox took over it, since clearly no one else was doing a proper job of it. All the glass was shattered in the Twelfth Night plot with Blodwen, but was replaced... um, sometime. There's an apple tree (for protection against the Dark) growing by the front door now. Audrey II and Stitch knocked a hole in a pane brawling, but I that eventually got replaced too. To my knowledge it's intact nowadays, isn't it?

Anybody want to help fill in the gaps here?