I don't think there is any plant that wouldn't do some damage to a wooden fence.

I think this is about the 23th or 24th post I've read tonight asking gardening questions and no info on where in the world they're located. Not a very serious gardening site I guess.

You just need to find a vine that loses its leaves in winter and doesn't attach itself to the structure. Climbing hydrangea fastens itself using roothairs along its stems that adhere to whatever surface it is climbing so that's no good. A honeysuckle could work but prefers a lot of sun. I'd consider a clematis - there's dozens of choices and many varieties are quite shade tolerant. And like the honeysuckle, it wraps its tendrils around the supports and can be easily removed. Plus, most should be pruned each spring anyway.

And I'm not sure how critical location is to this issue - many vines are adaptable to a very wide range of climates and locations all over the temperate parts of the world. Clematis can be grown from zone 3 to zone 10.

Many participants are new to Garden Web, even if longtime Houzz members. The old GW format routinely asked for location or zone - Houzz does not. And new participants may not be aware of the significance of revealing their zone or location.

Some say Lonicera tellmanniana tolerates and blooms with some shade. I have not grown it and knowing zones is really critical.

I am in zone 6 (near Boston MA) although some say you we should consider ourselves zone 5. Thanks for the comments. I am having second thoughts about growing a vine up a fence, as much as I want privacy from our neighbors. I may just use my own trellis. Which clematis vines grow well in the shade? I have never had luck with clematis vines in shade.

look for vines that twin and don't have airal roots like ivy or stickers
maybe some thing like this http://willamettewildlings.com/documents/DP-SPDO.pdf

I meant Lonicera hispidula pink honeysuckle

Lonicera hispidula is a west coast native vine and to my knowledge, not readily available commercially.

There are many different types of clematis that will thrive in just a couple hours of direct sunlight. Check out this link: Shade tolerant clematis.