Yes you can find tailing Reds in the shallows during the winter. You need to wait for the weather fonts & warmer days heat up the shallows during the late mornings & afternoons.
There are a few Kayak rental places in: Beaumont, Galveston, Rock Port, & Aransas Pas. Most of the rental shops will supply you with a kayak, paddle, seat & PFD. You need to provide the fishing extras. I can show you how to add a rod holder to a small cooler which will have you ready to fish.
Were are you from? I can meet you anywhere between Tyler & the Coast. I would be interested in next weekend or the weekend of Feb 4th, weather permitting. (ie. if there is a NE wind the fishing if OFF) Call me at 903-565-4728 or e-mail me email@example.com