Bagworms don't produce cobwebs. Pictures may help us figure how what you do have. It sounds more like tent caterpillars or something like that.

The mistletoe may be weakening the trees to the point that they are more attractive to whatever insect you're dealing with.

any chance of images?

If a Hackberry becomes invested with mistletoe, it can die in a very short period of time. Usually the tree has too be so invested that it is almost evergreen in the winter. So, are the cobwebs on the foliage or the mistletoe? Either way it is only aesthetically a problem. Mistletoe is the bigger issue.

The cobwebs may only be an aesthetic problem, but, depending on what's making them, their source may represent a serious threat to an already stressed tree.

I can guarantee you they are under stress right now. The area has had over 20 one hundred degree days and counting with no rain. I understand the value the shade provides but even weed trees need some TLC every now and then. You can thank the birds for planting them in fence rows and under power lines etc... The best you can do is evaluate the situation and be proactive depending how long your going to be there.

Thanks, friends. I have found out that it is "webworm" which is really the worms that turn into moths. I was told they will not kill trees, but I do need to spray in the spring to keep them from coming back. The poor Hackberry is suffering terribly. I have been watering it, and I keep telling the estate agent that it is going to die if we do not help it, but he does not care. You know the type...they do not care what happens at a rental property so long as the rent and the rent increases are paid and the tenants are not tearing the house down brick by brick. It makes me totally sick, but I cannot afford to pay to have the tree pruned. I was told it would cost around $300, and it is just not in my budget. : (