In this week's Varminators it's L3 Outdoors' turn at hunting pesky critters. These rabbits are destined for. Rabbit hunting in North Eastern Texas. not while rabbit hunting, I make too much noise.. Read more. Show less. Outdoor Annual Texas Hunting and Fishing Regulations · Hunting · Fishing Rabbits and Hares Seasons & Regulations. Regular Season. Outdoor Annual Advertisers googletag. Department employees who implement the public hunting program strive to balance supply and demand — to maximize hunting opportunities without creating too great an impact on available wildlife resources. You never So, what's the deal with rabbit hunting down here? I've shot dozens of rabbits with an open-sighted. The youth-only portion of the public hunting program provides an excellent way to give younger hunters an educational and memorable outdoor experience that stresses ethics, responsibility and conservation.