They are fall webworms...a close relative of the eastern tent caterpillars. Fall webworms make their large tents on the ends of branches and become quite common in the summer. Mulberry is a favorite host, so much so that in some locations they are called Mulberry Caterpillars.

The best recommendation (not just mine) is to disturb that webbing with a broom handle, stick, or something like that. Just by opening the nest up, you'll put those caterpillars on the dinner table for the host of predator animals and insects the prey on them. The parasitic insects will be able to get at them, too.

If there are any nests that you can reach with a pole saw, you could remove them and dispose. There are no chemicals that are recommended for these kinds of caterpillars, as their nest pretty much protects them.

Just let all of their natural enemies have at 'em. Don't be surprised if you begin hearing lots of bird squawking in the very near future! They love those things.

Thanks for the advice. I'm sure the birds will love them.