starlysh Your graphics settings mostly look fine, although I'd suggest turning High Detail Lots down to 2 or 3 for performance reasons. Your GPU can handle higher, but the game engine cannot.
Just as a test, try moving Options.ini (in Documents > Electronic Arts > The Sims 3) to the desktop, which will reset your in-game options, graphics and otherwise. Don't change anything other than resolution and fullscreen/windowed; just load a save and see whether the snow is still missing. If this doesn't help, you can delete the new Options.ini and restore the old one.
I doubt this is related to your unrecognized graphics card, but if you do want to get it recognized just to be sure, I can help with that. Let me know.