I haven't found a good resource online regarding this subject, so I'm posting the information I have researched regarding the appropriate licensing requirements for a Morgan 3 Wheeler in Texas.
1) Texas considers the Morgan 3 Wheeler a motorcycle for licensing purposes, you will need an "M" (motorcycle) endorsement on your license to drive a M3W legally in Texas.
2)To get an "M" endorsement you need to take a private "Basic Riders Course" that is offered at many places across the state, like here:
http://www.motorcyclerentalshouston.com/miscpage_010.aspNOTE: You can take the Basic Riders Course on either a conventional two wheeled motorcycle, or on a 3 wheeled motorycle-type "trike" like a Can Am Spyder (Two wheels in front) or a Harley Trike Conversion (1 wheel in front). You CANNOT take the basic riders course in your Morgan Three Wheeler. Many "trike" courses have trikes available for you to take the course on - usually Can Am Spyder's.
3) After you take the course (which is given over either two or three days), you recieve a certificate, which you take to the Texas DPS office. You then need to take a short written test, if you pass, you are given an "M" endorsement on your license and can drive a Morgan 3 Wheeler legally in Texas.
Texas has no helmet law for adults driving either Motorcycles or Trikes of anykind.