If you like flowers also, the evergreen clematis Armandii is very beautiful all year, and has fragrant flowers once a year as well.
It is very popular in the Pacific Northwest, where I used to live, it doesn't do well for me in drier part of California (zone 9b)where I am now. But still my favorite evergreen vine.
Pea

Trachelospermum jasminoides is evergreen and fragrant. It is less rampant than Clematis armandii and more suited to growing in a container. I don't know what your winter lows are but Solanum laxum 'Album' is evergreen although the flowers are not fragrant.