Dead trees increase the danger of tree felling in several ways. The limbs above you are much more likely to break off, the wood may be weakened making the hinge more likely to break, there may be voids inside that you cannot know about until the tree is already falling, the tree can start falling at any time because it is weak, even when just cutting the notch. And the list goes on, so be careful!
I cut down several dead trees in this video, mainly because they are likely to end up falling on my driveway, and also I use them for firewood.