Are the vines still alive? That's the first thing to tell us.
Urushiol (the toxin that your body reacts to) is most strong in the woody parts of the plant and takes quite a while to dry out of there. If you lop off the vine at the base and let it die, the leaves will dry up, fall off and with a couple of rains probably not cause any harm. The woody parts however, like I said, take a while...so proceed with common sense and caution.
Yes, during the winter they're not nearly as nasty as in the spring and summer, but if you start chainsawing and have chips hitting your face, you better plan to take a shower no more than a couple of hours of work, or you'll be in for an uncomfortable time!
When I bought my place and cleared out the poison Ivy from the property I cut the vine at the base and let it die. Then I went back to the tree the next winter and pulled the vine off and tossed it in the woods. Came back inside, placed all my clothes in the washer and took a shower. Never had a problem.
Since the trees you're asking about are already dead, the bark may be loose and you may be able to pull it off now. Just wear stuff you can easily wash while taking it down...then change your clothes and any areas of skin you think may have be exposed and then go back to firewood duty. That's what I recommend.
Hope this helps