I'd avoid the ivy as it can be difficult to control and is invasive in some parts of the country.

Here are some links from the clematis forum on evergreen vines in your zone:

http://forums.gardenweb.com/discussions/4139399/evergreen-for-zone-7?n=3

http://forums.gardenweb.com/discussions/3935500/evergreen-clematis?n=7

Lonicera sempervirens (native coral honeysuckle) is often at least semi-evergreen in Z7. It sometimes manages to push out flowers in winter too.

I think your options are somewhat limited :-) The Bignonia is unlikely to be evergreen in your climate and the gelsemium will be of marginal hardiness, as will be any of the common evergreen forms of clematis. And I cannot in good conscience recommend English ivy anywhere!!

I think your best solution would be one of the selections of Lonicera sempervirens, trumpet honeysuckle. This is a native plant, quite cold hardy, attractive to hummingbirds and should be at least partly evergreen in your climate.

Thanks everyone! I just googled the trumpet honeysuckle and it is lovely, so I think I'll start there in the spring and see how it goes. Given the sneakiness of English Ivy, it may end up on my fences by spring if I like it or not!

The reference to Gelsemium sempervirens flowering in the Winter piqued my interest and raised suspicions. NHBabs could you link to the picture on the NH Forum? I could only find one which appeared to be growing indoors. We can't grow it over here, despite winters much milder than NH and when I Googled it it seems to flower in June. I wonder if it was actually Jasminum nudiflorum if it really was blooming in the winter?

Floral, here's the photo that made me think it blooms in winter, though this was late December of a quite mild winter here in New England:

http://forums.gardenweb.com/discussions/3580557/strange-weather-odd-photo?n=10

Here the same poster, Bill_RI (zone 6b,) shows G. sempervirens Margarita at peak bloom in late April and there are other references to it starting the main bloom in early April.

http://forums.gardenweb.com/discussions/2038306/show-us-your-gardens-a-photo-thread-april-2012?n=28

The first photo does indeed show Winter Jasmine ie, Jasminum nudiflorum, as I suspected. Later in the thread the OP names it as such. But the second, taken in April is Gelsemium sempervirens, so the June bloom period I found on line is clearly not accurate for that region.

Thanks for clarifying, floral. I clearly didn't read carefully.

Would the Jasminum nudiflorum also be a possibility for the OP?

Is really not a vine at all but a very laxly growing shrubby plant. So it doesn't really "vine" or attach to fence or trellis but could certainly be trained to sprawl on one :-) And it is not evergreen.....winter flowers appear on virtually naked stems/branches.

Thank you - I will look into the Margarita! In the meantime, I spent some time "excavating" along the fence line today, just to see what was there. The vast majority of the current vines originate in my neighbor's yard, and I'm fairly certain they're a mix of Porcelain berry and Virginia creeper, plus possibly other stuff. However, when I raked back all the layers of leaf mold, I also found lots of English Ivy growing along the base of the fence (at least the one on the north side of the property). Nice to know it can grow under cover . Once spring rolls around, I'll clean that area up a bit more thoroughly and see what can be done. I'm not sure I'll be able to convince the neighbors to do anything about the Porcelain berry. Their entire yard is a huge mess so I fear there will always be weed creep...