Since I wrote my initial post we have visited Zion, Bryce, Capital Reef, Canyonlands and Arches National Parks (and had a great time, I might add). The tent caterpillars were only evident at Zion. Fortunately, they were minimal and stayed "where they belong" in their tents, in the trees. Oh, there were a few that crawled into our wheel well and onto our hanging laundry, but nothing really bothersome.
When we returned, I told my 91 year young mother about the tent caterpillars and she promptly shared this story. When growing up in New Jersey her brother, Ben, got an award for collecting the most tent caterpillars at school! Perhaps that's what we need, a caterpillar collecting contest at the campground!