I have a tree with a fairly heavy growth across its trunk and branches; I suspect that it's a form of lichen but I'm not sure.
Is this something that will negatively affect the growth or health of this tree? Should I spray it down or leave it be?
These look like the tree lichens that are growing on my own trees. A lichen is a composite organism where by a fungus lives together with an algae in a symbiotic relationship. They don't hurt the tree, and are more commonly seen on the bark of older trees where the bark is not constantly being shed and regrown. So, it may also be an indicator of poor health if a younger tree is not growing as well as it should.
Although more common in damp areas, they can require very little moisture to grow, and do better in clean air.
As Graham says they are lichen and moss. A tree will commonly live in a symbiotic relationship with millions of macro and micro-scopic organisms. In tropical and temperate rain forests overgrowth on the the bark is very common.
That they are growing so well indicates good things about the environment!
Lichens are a marker for air purity. They vary from algal lichens to the mossy shrubby lichens you will see hanging from the branches of pristine forests. The more complex organisms they are the purer the air. They're very good to see close by.