I live in Greater Vancouver and have a plum tree with a few large branches which produced hardly any leaves last summer. I'm noticing this spring that the same branches won't be producing many leaves since the buds look somewhat "burned" or "dry". Should I prune those branches? Am I too late into the winter season to do so?
Yes: saw them out, they are dead. Use under-cutting to prevent them from tearing down the trunk when breaking free (cut part way through from below, out a short distance from the trunk, then cut from above, beyond the first cut. When the branch falls due to the second cut it stops tearing away when it reaches the first cut. Then you can saw away a short stub, just beyond the branch collar, ending with a perfect result instead of part of the bark being ripped away by a falling branch).