To the first part of the question: depends. In some cases, while open carry is fine, once the long coat is on, the gun is concealed and would become a no-no. And a lot of places have regulations about transporting a firearm–in Texas, for instance, any citizen with a right to own a gun can carry a loaded one, concealed but ready, in their car. It’s the so-called “traveling” exemption (basically, if you’re traveling, it provides an affirmative defense to prosecution.) Other states aren’t so lenient.
As far as “concealed,” I don’t recall whether there’s a statute in Texas law that defines it, other than applying the ‘reasonable person’ doctrine–if a reasonable person can’t tell you’re carrying, then it’s concealed.
This leads, of course, to discussions within the CHL community about whether “printing” is illegal. The consensus is, in Texas, that it is not illegal. For example, in the summer I wear an untucked tee shirt over my gun. If you look closely, you can see the outline, though because of the nature of the holster and its cant, it doesn’t scream “OMG GUN!” In fact, since I’ve gotten my BlackBerry, I’ve noticed that the BlackBerry creates a vaguely similar ‘bulge’. Or, I’ve heard it argued, it could, to the average observer, be a medical thing–a diabetic pump or some such.
The only very bad thing I can think of is a crime called “intentional failure to conceal,” which obviously requires the element of intent. I mentioned in the other thread that I once accidentally tucked my overshirt behind my gun, meaning the gun was exposed at Wal-Mart. Even though the gun was visible, I wasn’t guilty of the crime, because I wasn’t intentionally failing to conceal. Whether a police officer would have seen it that way, I don’t know, but I feel pretty confident that a jury would have seen it for what it was, had it gotten to that. Same thing goes for a gust of wind lifting someone’s shirt. It happens from time to time.