Grape vine will lose its leaves in winter. It's going to be hard finding an evergreen vine in your zone, especially if your situation is in the shade. I found this online:
Evergreen Vines
Many evergreen plants contain an oily resin or other toxic compounds, but you'll find a few nontoxic choices for your trellis. Japanese honeysuckle (Lonicera japonica) grows in USDA zones 5 through 9, producing fragrant pink, yellow or tricolor blooms. The plant is a vigorous grower that needs aggressive pruning, and it's considered invasive in some areas. Hardy in USDA zones 5 through 9, five-leaf akebia (Akebia quinata) produces clusters of purple blooms and semi-evergreen foliage.
Plants to Avoid
Wisteria (Wisteria spp.), which generally grows in USDA zones 5 through 9, is lovely, but all parts of the plant are poisonous to humans and pets. The seeds, in particular, are highly toxic, and even two seeds can cause serious illness if eaten by a young child. Clematis (Clematis spp.) grows in USDA zones 5 through 9, but it is toxic to cats and dogs. Both English ivy (Hedera spp.) and Boston ivy (Parthenocissus spp.) are toxic to both people and animals and may be invasive, too. Hardy in USDA zones 5 through 9, these shade-loving vines can cause serious illness.
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