I'd basically go for the method you describe yourself, but with an added white spraypaint straight onto the grass for the patches. make the spray painted areas somewhat smaller than the intended snowy area, so you can create a bit of a fade into the grass when applying the snow.
Oh; and don't forget to add snow to your trees, tree bases etc, to maintain the effect.
Also, make very sure that the glue you use is either clear or white, and does not yellow over time!
But I also really like SteveBurt's idea of using patches to add or remove from the board as you see fit; it will give you a lot of versatility, and I would actually prefer that over a permanent setup. You could even arrange for a removable snow cover on the roofs of buildings in that way!
But I would personally go for a different material than felt. Felt would be durable, but using some very sheer white cloth, maybe fully synthetic, that would drape over any surface easily, would work better I feel (mind; I have not tried this! (yet)).
You could then still use snow flock on top of that, to get the effect across better. Perhaps even christmas decoration snow spray cans could work for this?