Groundcovers tend to be used to cover large areas in the landscape. If deer are a problem for you, the last thing you need is to plant a ground cover that becomes their feed lot. So, consider planting of the following 3 groundcovers which are not usually top snack choices for deer.
Bugleweed, or Ajuga reptans, forms a 6-9 inches high, mat-like ground cover which is so dense it chokes out weeds from growing through it. Hardy to Zone 4, it does well in sun or shade and tolerates poor soil. Because of its tendency to spread by stolons, Bugleweed should only be planted where it has room to grow. It's best not to use it as an edging near grass as it will quickly spread into the lawn. Plant Ajuga in areas with good air movement to help avoid disease problems. Also, dividing it every 2-3 years is recommended. With a multitude of cultivars on market, Ajuga reptans is a ground cover that can provide a rainbow of flower and leaf colors providing four seasons of beauty in your landscape. Flowers area usually violet-blue but sometimes are red, white or purple. Foliage is attractive year round and selections with green, bronze-purple, deep purple and multi-colored foliage with variations of green, white, or pink are readily available.
Pachysandra terminalis is your best choice for heavily shaded areas. It's one plant that prefers the shade and can actually discolor, turning yellow, with too much sun. New leaves are light green and mature to a lustrous dark green. Commonly known as Japanese Pachysandra or Spurge, this Zone 4 evergreen groundcover performs better in northern climates than southern. It is a slow grower reaching 6-12 inches in height and spreads by rhizomes, forming a solid mat. It likes moist, well-drained, acidic soil with a pH of 5.5 - 6.5. 'Green Carpet' is a preferred selection of Pachysandra as it gets 4 inches tall, has smaller leaves that are darker in color and does not trail but instead just grows close to the ground.
An extremely hardy evergreen ground cover, Vinca minor or Common Periwinkle, can be planted to Zone 3 but goes even further north if protected by snow. This low-growing, ground-hugging plant gets 3-6 inches in height and has yellow-green new growth which turns bright green with age. Best of all, this prostrate mat provides color to your landscape with attractive, 1-inch diameter, lilac-blue flowers in March and April and sporadic blooms afterwards. Vinca will flourish and fill in quickly in moist well drained soil. It tolerates poor soil however it won't spread nearly as fast. It likes full sun but will do better in shade just not dense shade.