As the Supreme Court noted in District of Columbia v. Heller, the 2008 decision recognizing a constitutional right to armed self-defense, "the majority of the 19th-century courts to consider the question held that prohibitions on carrying concealed weapons were lawful under the Second Amendment or state analogues." In 1850, for example, the Louisiana Supreme Court upheld a ban on concealed weapons, ruling that the right to bear arms protected by the Second Amendment applies only to openly displayed weapons: "This is the right guaranteed by the Constitution of the United States, and which is calculated to incite men to a manly and noble defence of themselves, if necessary, and of their country, without any tendency to secret advantages and unmanly assassinations."
Openly carrying a weapon was considered manly and honorable, while secretly carrying a weapon was considered sneaky and disreputable; someone who hid his weapon was probably up to no good. Today, by contrast, the prevailing view, at least among urbanites, seems to be that secretly carrying a weapon is less worrisome than carrying it openly. Out of sight, out of mind.
Although their constitutional position has a long pedigree, organizations such as Open Carry Texas, which seeks "to condition Texans to feel safe around law-abiding citizens that choose to (openly) carry (guns)," may be fighting a losing battle. In any case, concealed weapons are probably a more effective deterrent to crime: When guns are hidden, bad guys do not know which potential victim might be armed. Hence there is a practical advantage to keeping your gun out of sight, aside from avoiding a panic at Starbucks.