Answer: Native plants are usually more deer and bunny resistant than other commonly grown plants so you might lean in that direction. Some suggestions include:
Sweet Woodruff (Galium odoratum) - 8" tall, zones 4-7; partial shade to full shade. Woodland ground cover spreads by rhizomes. Star shaped scented leaves encourage the deer to pass by. Small white flowers in spring. (critter resistant)
Dead Nettle (Lamium sp.) - 4-6" tall, zones 4-9, partial to full shade. Colorful
leaves and tolerance of ordinary soil make this a popular ground cover. Silver
leaves lined with green with white flowers in May-June. (critter resistant)
Epimedium x perralchicum 'Frohnleiten' is a sturdy, quick establishing, low maintenance groundcover for the shade. It performs well in moist, organic soils and even in difficult to handle, dry shade locations. For fast coverage, plant 3" pot-sized plants 6" to 8" apart. Plants spaced 12" apart will fill in more slowly as the plants produce runners. Cut back in the spring; use a lawnmower in large areas. Bright yellow flowers appear soon after, then the fresh green foliage with a red edge resumes growth and remains evergreen throughout the year.
A final suggestion is Pachysandra terminalis (Green Carpet Pachysandra). This is an evergreen, clump-forming ground cover with dark green leaves; variegated varieties have cream margins. It spreads, but not aggressively, by underground runners and thrives in full shade. 'Green Carpet' is more compact, with smaller, finely toothed leaves, to 3 inches long.
Hope one of these suggestions is just right for your landscape.
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