A. Unfortunately, there are only a few vines that keep their leaves all winter, and they do not have any flowers. One suggestion might be to plant an evergreen in front of your trellis, which would give you privacy year-round. You could then grow one of the many beautiful flowering vines behind it.
You did not mention whether the area receives a great deal of sunlight, or if it is in the shade. This would affect your decision on the type of vine you would like to plant. If there is not enough room for an evergreen, or if you really do not want one, the only vine that would remain evergreen would be English Ivy Hedera helix. The plants are very vigorous, can quickly spread to form a dense patch, or form aerial roots to climb up vertical surfaces. Cold, dry winds or full sun may cause scorching in the winter, so your site should be sheltered. If the plants get out-of-control, they can be clipped back at any time. Although you will not get flowers on the ivy, there are many varieties with variegated leaves, such as "Little Diamond," which is grey-green in colour with a creamy white edge. "Thorndale" has small, leathery, dark green leaves with prominent white veins, and a bronzy-red winter colour, and "Glacier" has small, dark green leaves with creamy-yellow margins. Although you would not get the flowers, you could have very attractive foliage.
Zone 5 director
Master Gardeners of Ontario