Poison ivy attaches itself with dark, hair like aerial roots that may have a slight reddish cast:
Photo Source: Wikipedia
Before it gets to that state, though, the hairs start off small. The following is of my test plant. It is starting to send out vines and therefore is growing these roots. From a distance, they look like hair. Close up, they look like small, woody pieces.
This is another test plant I had a few years ago that started to do the same thing. Notice how there are some roots that really look like hairs and some that look soft:
Why does poison ivy climb? According to Smithsonian Science:
"What triggers a poison ivy plant to climb is a mystery. Some poison ivy plants climb right away from seedlings and others do not. Individual populations of these plants often contain a mix of climbing and non-climbing plants."
When the vines get old enough or thick enough, they can cover an entire tree trunk. Unlike some other plants that can kill the host tree, such as the strangler fig, these vines rarely cause a problem. They can grow to the height of a the tree and even look like the tree.
There are many of these vines where I work. When our crew encounters them, they cut a 6-8 inch piece out of them. This will cause the plant at the top of the vine to die, but it can take a while. They generally just leave the bottom part and it rarely grows back.
That being said, if you choose to remove a large vine, be careful. Clean your tools completely when finished. I have read that extremely small droplets of urushiol oil can spray out when cutting a vine or breaking a root, so clean yourself, your clothes, and your shoes.
The best advice is to get rid of the plant before it starts climbing. However, since the plant often grows mixed well with others, it can be hard to tell what it's up to until it's climbing.