My apologies if someone already entered this above. I think someone did mention tanning skins, but I wasn't sure about the rest of this definition from www.yourdictionary.com:
Main Entry: 1.taw
Pronunciation: 'to
Function: transitive verb
Etymology: Middle English, to prepare for use, from Old English tawian; akin to Old High German zawjan to hasten, Gothic taujan to do, make
Date: before 12th century
: to dress (skins) usually by a dry process (as with alum or salt)
It also said the first use of taw to mean playing marble was in 1863. Another interesting meaning given was that of square dance partner. Maybe that would go along with the cowboy references?
Here are some other sources which might lead to some answers:
Dictionary of American Regional English (Project)
Great thread!
kat