I suggest Mazus repens, or Laurentia fluviatilis. I grow both, and here, in zone 7a, Mazus is ground-hugging and evergreen. this Winter will be my first for trying to over-winter Laurentia (the Blue Star Creeper).
Another plant, quite amazing, is the Selaginella uncinata, which is supposed to be hardy in zone 6. I have my doubts about this. I also like Parochetes communis, and the baby blue form of the Australian violet, but both are tender plants and the latter almost impossible to find.
In a dry, Sunny area, Juniperus 'pancake' would thrive, and it is about as flat as the name would indicate.