Having it in one's hand (but out of sight) when going to the door? Think about it. Just what would one intend to do with it? Should the visitor prove to be really dangerous, one does not want to be standing right in front of him.
Since I posted that I did recently go to the door armed but with the gun not visible from outside the door, I'll answer.
As previously noted, I have security doors, so I can open the wood door without the person outside being able to come in through the door. Two scenarios that could possibly have played out after someone trying the security door (NOT knocking or ringing the bell):
1. person at door is trying to hide from police helicopters because he just committed a crime nearby, waves gun at me and threatens to shoot me if I don't let him in. In which case I believe I would be justified to shoot immediately, which I would do through the security door.
2. person at door is either trying to hide from police as in scenario #1 or is mentally ill; either way on being denied admission through the door would dive through the window which he could reach in two steps, much quicker than I could get anywhere safer. In which case I would shoot if he broke the window and started entering, possibly first trying warning him I was armed, depending on how scary he looked and how he was behaving -- if he just looked confused that would be a lot different than if for example he had a knife in hand.
Thankfully neither of the above occurred, the "visitor" was apparently looking for a house he could just walk into, but I don't regret having been prepared.
To put this in context, one morning around 9 am within one or two days of this experience, the following occurred at the 7-Eleven around the corner: BG takes beer and sandwich without paying, female clerk follows him outside to try to get paid, BG stabs her, male clerk rushes outside to try to rescue female clerk, BG stabs him also, then runs away. Male clerk died, female clerk was in critical condition last I heard, BG was caught a few blocks away a couple of hours later. G-d forbid, but it could easily have been my house he tried to hide in.