This is not the thyme that you use in the kitchen, but a woody perennial that will reach 2 to 3 inches in height. The leaves have the scent of thyme, but the scent varies, depending on the time of year. In the summer, creeping thyme will bloom with small deep-pink or lilac flowers. Creeping thyme is hardy to USDA zones 5 through 8.
Irish moss is a fast-growing ground cover that reaches just 1 inch in height. In the spring it will delight you with thousands of small, white flowers. Irish moss needs shade or partial shade and extra water during particularly dry periods. Irish moss is hardy to USDA zones 4 to 9 so it will do well in a zone 5 garden.
Another fast-growing ground cover, Kenilworth ivy blooms with tiny, lavender flowers. It will grow to a height of 2 inches and requires a shady location. This is a perennial, and it also goes by the name of pennywort. This groundcover will take a bit of cutting back to keep it from invading other parts of the garden. Kenilworth ivy is hardy to USDA zones 4 to 8.