Cut dead branches?

Short snswer: They should be cut out.

Unless you have a ladder, a chain saw, and the confidence to do it, you should probably call an arborist. Make sure he's credentialed; I've seen some really sad botch jobs. Because they are dead branches, it's ok to trim them out anytime. The arborist should give you some good advice on how to baby your baby to it's best health.

Honey Locusts are some of the most beautiful trees, but also a little on the delicate side. One summer my locust dropped leaves at an alarming rate, and an arborist recommended watering the roots - we were having a drought and a heat wave. I actually had the tool he suggested. It hooked up to the garden hose and had a 3 ft spike that put the water underground right where the tree roots were, with no loss of water from run off. It survived and is growing well.

Trees need good air flow all the way to the trunk. A wet trunk allows insects and diseases easy access. A general rule of thumb is to have limbs 18" apart. Do not have the lowest branch facing into the general wind pattern. For instance here in the Midwest our general winds come out of the southwest, so my lowest branch should not face southwest. The wind will either push it down, into my way when I'm mowing, or push it up and into the natural growth of the branches above it. In the picture, look at the trees on the right. They lean to the right in part because the predominant winds come out of the left.

The best advice I got on trimming trees: leave a knuckle, not a thumb. In other words, trim the dead thumb off, but leave enough on the trunk that the tree can naturally close off the damaged or dead part in the most healthy way for it.

Sorry if I went on a bit: class is dismissed.

If you cut them back while they are not dormant they will grow back

Thank you so much for all your help!