I have a Samsung Galaxy S3. I wanted to see what the "AT&T Messages" app was like. I did not like it at all. I followed the instructions above from SlappyMcgee - "Application Manager" --> "AT&T Messages" --> "Uninstall Updates". No "Disable" button came up for me. Probably the new Android version changed the "Uninstall" process for this app.
Anyway, after I clicked "OK" twice, it was uninstalled (at least the usage of the app). Since it is part of AT&T software pre-installed on the phone, it reverts back to the Factory version, which doesn't allow use until you activate it. You cannot totally get rid of it, but again, it cannot be used unless you activate it.
Now, I could go back to using the "Visual Voicemail" app, which I like much better. The "AT&T Messages" app is just too busy and convoluted with combining everything. I prefer everything separate. Nothing bad will happen if you follow the instructions in this post.