Thanks for the responses! I appreciate the help.

I live in the northwestern suburbs of Philadelphia, and I certainly
have quite some poison ivy. I was planning on doing most of the
cleanup starting in October, when a lot of the plants start going into
hibernation mode. Should be a lot easier to clean up without having to
worry about trampling underfoot.

My wife, in particular, loves all the butterflies that come around the
area, so I don't want to remove the foliage that attracts wildlife.
However, it would be nice to be able to walk around back there and
have something nice to look at from our deck, instead of a really
thick unruly underbrush.