Chances are, if your tree is truly dying, it's not your fault. Pruning during just about any time of the year, except when the plant is dormant in winter, merely stimulates new growth at the tips.
The problem with pruning right before winter is that, as with all pruning, tender new growth is stimulated and since that tender new growth is happening in fall, it doesn't have time to harden off. It's more likely to get nipped by winter's frost. However, this should not result in the death of the tree.It's possible that what your tree has is severe winter burn and is not dead. Winter burn is what happens when cold winter winds dry out and damage the needles or leaves of a plant, particularly evergreens. In spring, when the plant should be sending out new growth, instead small or large portions of the plant turn brown from the damage.If the winter burn problem is mild, just trim it off. But if it's severe and the evergreen is not a yew, holly, or boxwood (all of which can be cut back hard), you may have to chalk it up as a winter loss and remove it.