Roses are not really evergreen. And any evergreen jasmine will be very iffy hardiness-wise in zone 7. You can try Clematis armandii.......it is evergreen and has a plethora of fragrant white or very pale pink blooms in early spring but will also be of marginal hardiness in zone 7.

I really think your best bet would be our native Lonicera sempervirens or trumpet honeysuckle. It will remain mostly evergreen in your zone and has a very long bloom period with bright red-orange trumpet shaped flowers that hummingbirds love.

Lonicera sempervirens

Thanks gardengal! I would love honeysuckle, but my wife is under the impression that many people are highly allergic to it? I've never heard of such.

I've never heard of that either. They have a pretty low pollen count so do not contribute in that manner. There are some instances of the vines themselves causing a skin reaction - contact dermatitis - but everyone has a different sensitivity to this and if not actually touching the plant, it is really not an issue. And many other common plants have a much stronger reactivity in that regard.

I think that's what I'm going to go with. She might not even know what honeysuckle looks like.

Does anyone see any reason for a trellis or anything to train it up the fence?

It will not stick itself to the fence. You'll need trellis or wires.