Ask Mr. Smarty Plants

Mr. Smarty Plants isn't very familiar with caterpillars, but from your measurements I'd say that it is too short to be an inch worm.

But lets get to the plant part of the question and see where that leads. The common name Prickly Ash is applied to at least three plants found in Texas: Aralia spinosa (Devil's walkingstick), Zanthoxylum hirsutum (Texas hercules' club), and Zanthoxylum fagara (Lime prickly ash). I don't know which one you have, but Z. hirsutum is a larval host for the Giant Swallowtail butterfly Papillio cresphontes. Check to see if the images match the caterpillar that is chomping on your tree. (more info and images)

Zanthoxylum fagara is the larval host of Eantis tamenund the Sickle Wing Skipper. The caterpillar is light green, but it lacks the dots that you mentioned. 

So we have two possible suspects, but no positive ID. You might want to contact the folks at the Fayette County Office of Texas AgriLife Extension for some help closer to home.

The caterpillars should pupate before too long which will halt the onslaught on the tree. Will the tree leaf out again? This depends on the extent of the damage. One word of caution however; when people see a tree in distress, the tendency is to give it lots of water. Please refrain from doing this. The leaves on a tree help to move water from the roots up to the stems. When the leaves are missing, there is a possibility of the roots becoming waterloged through overwatering.