If hunting is allowed in your county, Harris, Waller, and Fort Bend all have hunting seasons listed in the 2007-2008 Outdoor Annual Hunting and Fishing Regulations, then it would be up to city ordinances. I seriously doubt that the TPWD can or will track you local ordinances.
I think the question would actually be whether they allow shooting in the city limits. I don't think they could allow target practice with a bow, but ban hunting with one.