A lot of the wood that I cut has been down for a while, especially the ash. Oftentimes the bark is easily removeable and when this is the case, I always remove it--PI or not. If the bark is solidly attached, then removing it would take way too much time. In this case, I would remove the vines with gloves on and call it good. On trees with deep grooved bark, such as ash, those vines can be a real pain to remove! If it is just too much trouble, I will just skip it and find another tree to spend my time on. Poison Ivy is miserable stuff. If you are unfortunate enough to have a bad reaction to it, it will consume your every thought.
I'm usually on track getting it a few times a year luckily I don't get it to bad but it's pretty unavoidable between digging, time spent in the woods and of course tractor tires. The stuff grows all over around here in fact I've got about three cord of ash and mixed logs from some cleared land which have quite a few small vines I usually just catch an end and peel them off with my hatchet or grab them with my fingers and they peel off pretty easy. As far as burning some still on the wood it's pretty dry by the time it hits the stove and that's even if there's any left so I don't worry much and the stuff that makes it in the stove is pretty small anyway. That being said there's stuff called Tecnu that I like it's a wash that you scrub with if you've been in it and I use it even after you get it. I think the main ingredient is deodorized mineral spirits but it works pretty good.
