That is a good question, and a very difficult one to answer. Deer especially tend to browse plants to varying degrees depending on how hungry and desperate they are!
Here are some groundcover choices to consider:
Prostrate Rosemary (Rosmarinus officinalis Prostratus)
Trailing Lantana (Lantana montevidensis)
Germander (Teucrium chamaedrys)
Gray Santolina or Lavender Cotton (Santolina chamaecyparissus)
Green Santolina (Santolina virens)
Thyme (Thymus spp)
Wedelia (Wedelia trilobata)
If the animals are not too hungry then these may also work:
Asiatic Jasmine (Trachelospermum asiaticum)
Carpet Bugle (Aiuga reptans)
Monkey grass (Ophiopogon japonica)
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