I emailed the Texas Parks and Wildlife Dept. and they replyed with the following.

Motor Vehicles Are Prohibited In Texas Navigable Riverbeds STARTING JANUARY
1, 2004

* The Canadian River and Prairie Dog Town Fork of the Red River are
exempted.

* A motor vehicle is defined as "any wheeled or tracked vehicle, machine,
tractor, trailer, or semitrailer propelled or drawn by mechanical power and
used to transport a person or thing."

* A navigable river or stream is one that "retains an average width of 30 or
more feet from the mouth or confluence up."

* The public retains constitutional right to travel navigable waterways, as
long as a motor vehicle is not used.

* It is illegal to obstruct, restrict, or interfere with lawful public
recreational use of a navigable river or stream.

* Crossing private property without permission to access a river or stream
is illegal.

* Local River Access Plans may allow motor vehicles in specified river
areas.

* Texas Parks and Wildlife Deptartment is seeking grant proposals and sites
for off-road vehicle parks.

They also suggested I contact the Bureau of Land Management in Oklahoma
since the Red River up to the state line of Texas is regulated by laws
applicable to Oklahoma.

As soon as I get their reply, I will post it here.