holes in tree
Yes, those are woodpecker holes, but the woodpecker is probably not the problem. Chances are that they are pursuing borers or other insects in the tree. This can mean that part of the tree is already dead or it is infested.
The holes look large and may be those made by a pileated woodpecker.
Here is more info on woodpeckers in the landscape: https://extension.umd.edu/hgic/woodpeckers-and-sapsuckers