Stoble,
Great question and the answer is yes! As a few others have mentioned, the Guadalupe River below Canyon Lake is cold enough to support trout throughout the year. Action Angler in New Braunfels can provide info on the best spots, best flies, as well as any gear you might want to pick up.
Three buddies and I fished the runs behind the L&L Campground yesterday and we all caught at least one. We were all using 5 or 6wt rods. Egg patterns, san juan worms, stone flies, and chartreuse streamers were working for us. If you go, get there early as there are quite a few fly fishermen and women from the Austin and San Antonio metro areas.
Check this website:
Rainbow Trout Stocking Schedule
There are plenty of spots around the Austin/ San Antonio area. Here's a little gem I would recommend. Take a day trip to Castell. It's about 2 hrs west of Austin on Highway 71. Its a great drive through the Hill Country and there are roughly 2500 freshly stocked rainbows in the Llano River awaiting your flies.
Fishing in Castell is best documented here:
Die Fische
Read the story "Forty Trout and Rising." I have been out there twice in the last 10 days and I used my 1wt and my 3wt. The trout are not as big as the Guadelupe (the largest will be around 12-14 inches), but they are aggressive and will take midges, dries, and streamers. If you go, the burgers at the Castell General Store are worth the trip alone. And you will also have option of hitting the famous BBQ (Coopers, Inman's, etc) locations in LLano on the way home.
Trout aside, the San Gabriel, Barton Creek, the Colorado, the San Marcos, the LLano are all great rivers for largemouth bass, small mouth, and Guadelupe Bass.
Sportsmen's Finest in Bee Cave and Living Waters in Round Rock can provide products and guiding services/recommendations for all area rivers.
It isn't quite Wyoming, but we have some fantastic fishing options in the area.
Good luck!