They're known by several names: Southern Flannel Moth, Puss Moth (eww), Possum Bug, Perrito bugs, an Asp, Wooly Slug or Megalopygae opercularis  if you want to get technical.

During their caterpillar and adult life stages, they are actually quite cute, little fuzzy things. Even though they seem majorly pet-able, that cute fuzz on the caterpillar is actually venomous spines that cause symptoms that sound quite horrible:

The sting produces an immediate intense burning pain followed the appearance of a red grid-like pattern on the skin that matches the pattern of the venomous spines on the caterpillar. Swelling and sometimes also lymphadenopathy [swollen or enlarged lymph nodes] follow.
In addition to the characteristic localized symptoms, more general systemic manifestations may also occur including headache, fever, nausea, vomiting, tachycardia [abnormally rapid heart rate], low blood pressure, seizures and more rarely, abdominal pain, muscle spasms and convulsions

Yikes. No touchy.

Unluckily for Texans, Southern Flannel Moths are most prolific in Texas, especially around Dallas and in the western central parts of Texas. Luckily, they have natural enemies to keep their numbers in check, including good old flies that lay their eggs on cocoons, which hatch and eat the pupae. And you didn't want to invite them to your picnic.

Basically, if you see a fuzzy moth, don't touch it and you should be fine. If you do brush up against one, go see a doctor.

Here's an interesting video showing their pupae and metamorphoses so you know what to look for.