Cherry trees at least still bear fruit even with green leaves of Summer in the Greenhouse, but grass doesn't stay green, and wild trees go bare with snow on them still, which makes no sense.
Fruit trees in a greenhouse produce fruit year round. This is an intended mechanic. I'm not sure what you mean by the rest of it.
Here's a picture: see, the wild tree types act like they're outside going deciduous and with snow on them, and all my grass dies off exposing the boring tile floor texture. (I knew I should have posted a pic originally, so thanks for confirming I ought to.) Grass in the Greenhouse should be Spring green for a season then become Summer but never Fall, IMO. It should stay Summer indefinitely until you Scythe it down, then again be Spring for 28 days, then become Summer again indefinitely, each re/planting.
I've never seen anything like that, so I strongly suspect that is version-dependent. On the PC version which I have, the trees are in whatever season they produce fruit in, year round.
The trees with snow are not fruit trees, ShneekeyTheLost. They are the 'wild trees' that the first post refers to. Skinflint is saying that non-seasonal plants such as oak trees, maple trees, and grass, appear as though they are growing outside in the cold rather than in the warmth of the greenhouse.