But no tufts of yellow or orange on their backs?

They are moths, not butterflies.

I didn't see any tufts of orange or yellow. They are several feet above eye sight. What kind of moths do you think they are? We have had them before on a little tree we cut down. The tree always comes back.

The ones that initially came to mind were the Tussock Moth caterpillars that we tend to get an invasion of in the months of March and April. They can range from yellow to black with orange heads but also have 4 yellow or orange tufts behind the head. They are also what I would call "Commando" caterpillars as they tend to rappel down silk lines and land on you when walking under an oak, which tends to be their primary territory for food and egg laying. If the ones you're seeing are completely arboreal and lack the tufts, then they're probably not Tussock Moths, but I would still wager they're moth of some kind.

I had this going on a couple weeks ago. It was raining caterpillar poo under our big oak tree. From googling, it looks like they were army worms or tent moths, both natives. Not terribly desirable but your tree should be fine. If you google "caterpillar on oak tree" you'll see lots of pics and may be able to decide which yours is if not one of these suggested. Sometimes caterpillars are tricky to identify since they can change in appearance significantly as they grow.