dead is dead.. one would think timing wont matter ...

if this is DIY ... do you know how to do it properly ...

care to post a pic for conformation ...

ken

I also have this stuff on some of my trees and don't know how to treat them if it is harmful

whats on the trunk my be defined by where you are ... big city name ..

forget about the shape today.. in 60 years.. this wont matter ...

removal and healing of a proper cuts is what will keep the tree healthy .. leaving stubs to rot and perhaps start interior rot is the concern ...

odds are the stuff on the trunk is irrelevant.. unless it is spanish moss... or some down south affliction of which i dont know much.. hopefully someone else can chime in on that ...

i might also take the lowest 2 branches.. just for future shaping ... base on what i see of your situation ...

when you decide to remove them.. start by removing all hanging weight.. leaving only a foot or two .. and then make the final surgical cut near the trunk ... dont try to do it all in one cut ...

a good cheap tree saw is worth the investment ...

https://www.amazon.com/folding-tree-saw/s?k=folding+tree+saw

since you wont be using it all that often.. i dont know why you would need anything more than the cheapest basic saw .... unfortunately .. most garden displays are xmas now.. so it might be a bit hard to find one right now .... in person ...

ken

I think it's as simple as pruning off the dead. Make proper pruning cuts.

"I also have this stuff on some of my trees and don't know how to treat them if it is harmful"

That is lichen. Very common and completely harmless.

So I should cut the dead branches at the base of the limb and now is better than spring??

Doing it correctly I guess is what I am in search of before I attempt the cuts.

Saturn

Do some research on what is a 'branch collar' if you are not familiar with that term. Pruning cuts should be made just to the outside of this mark.

If the branch is of significant diameter (greater than an inch or two), make an initial cut midway along its length to remove the branch weight and avoid tearing.