Irish Moss (Sagina subulata) is very pretty, low, and hardy to Zone 4b.

How much sun and water do the areas get? And what's the soil like? How big an area are you wanting to cover?

I'm not sure Irish moss would take much foot traffic. Also, most ground covers can and do jump edging.

I suggest mother of thyme for 'gentle' foot traffic. I'm not sure how well it would work in a high traffic area. I'm sure others can tell you about that aspect.

Mine is planted in a mixed path of vintage bricks and pea gravel that gets around 10 hours of sun this time of year. It spreads about 3 inches a year so if you put several small plantings along a path, it would fill in rather quickly. I'm in the third year with this plant so it is quite hardy in my book.

The bricks in the path that are shaded by taller plants have filled in with moss. I did not plant it and assume it is due to the wet conditions this year. It's quite charming in that the moss forms around the letters and shapes of the old stamped bricks making them readable.

I should add, mother of thyme is very low-growing at about 1/2", fragrant and will grow tiny little purple and white flowers. Having experienced invasive plants, this little lady is very, very low on the scale in my situation.

Thanks for the suggestions. The north 3/4 of the area gets full sun in the afternoons most of the summer; the rest of the time it's all in heavy shade. The earth has a LOT of clay in it (so we already know we have to work sand, etc into it). Rainfall is unpredictable spring through early summer, and gets pretty sparse the latter part of the summer, so whatever I plant would have to be drought-resistant (we're installing a watering system for the gardens, but not planning on it for the pathways). All together, the path's square footage is about 800 square feet.

clay + sand = concrete

Organic material is a more effective way to ameliorate clay soil.

Creeping jenny grows fairly fast, is low enough to walk on without tripping, and can take foot traffic. It prefers full sun and it's bright yellow color will become greenish in more shade. Mine has gone wild this year, might be persuaded to part with some. You can check my trade page.

There's also a small, creeping campanula, a little slower growing, again full sun, that's quite attractive.

Some time ago, I saw a website selling 'walk-ables' or something like that...if you can find it, you can see what plants they use.

Again, just about any groundcover will jump the edging, depending on heights, so periodic maintenance will be necessary. Personally, as long as I can continue to get free wood chips, I mulch my pathways.