I setup a fixed gear Swift Folder in 2000 and that bike is still being used (although not by me). It works great, but the Swift doesn't fold all that small.

Bike Friday offers fixed gear bikes in their normal fold and in the Tikit. I expect that the Tikit would be a lot easier to fold since it has an integrated rear triangle. The NWT/normal fold changes virtual chainstay length during the fold.

Many folders were designed for internal gear hubs and have horizontal or track style dropouts making a fixed gear conversion easy.