Patti --
Any question about residence ought to be fairly simple to resolve. If the document cited originated in Texas, and certainly if a Texas county official wrote it, rest assured that the men on the list are citizens of Texas. It doesn't matter if they aren't on the 1860 census for the county in question.
As mentioned earlier, the document you cited sounds exactly like a county militia census. I'm sure you've seen many others like it. The county sheriff used these to help identify men who were eligible for militia service. For instance, if any of these men returned after discharge from Confederate service, they were eligible.
Place of enlistment is not always a correct residence. As you know, enlistment records for these soldiers include a record of the number of miles each soldier travelled to the place of enlistment. For that information, check the Confederate service files for these 17 soldiers.
As their regimental commander to November 1861, Col. James McIntosh of the 2nd Arkansas Mounted Rifles would be cited as enrolling officer no matter where the regiment camped.
As Bryan mentioned, once the "Texas Fencibles" entered Confederate service in July 1861, members were no longer eligible for militia service, nor were they "Texas State Troops".
If Capt. Hawkins and his men ever were in state service, you should be able to find a commission and correspondence in the governor's papers or the state Adjutant-General's records. The latter may also include a militia muster roll.
Just curious -- when you ask about legal descriptions, are we talking about a court document? Where else have you been able to locate legal descriptions of Confederate camps?