As I see it, this question revolves around three separate issues.
Legality: As I understand the law in Idaho, you could pass out drunk with a handgun visibly holstered on your hip without violating the law. That said, I would not put it past a DA to file a bogus charge such as reckless endangerment and try for a conviction. He might very well get it too, considering the deep-seated prejudices which many hold against both gun owners and drinkers.
Public Relations: Being seen at a restaurant having a dinner which includes a drink or two is probably an overall positive in this category. Being seen at a bar (even a sports bar) is probably an overall negative. (That does not mean one should not do it, I just do not see it as a positive action from a public relations standpoint.)
Logic: Carrying a gun (even when drinking) does not alter the nature of man. If one has violent tendencies, alcohol may exacerbate those tendencies, but for the vast majority of people, if you would not commit a homicide while sober, you will not commit one when drinking. We must not fall into the trap of equating carrying a firearm to being more dangerous. Firearms are not dangerous - people are dangerous. If you are unfamiliar with how you react when drinking, you should not carry. If you tend to get violent when drinking, you should not carry. If you can not remember what happens when you drink, you definitely should not carry. However, if you are able to drink alcohol and continue to behave in a normal fashion (albeit perhaps in a bit better mood) there is no logical reason why having a holstered weapon on your hip would increase the danger of the experience.
The one situation where drinking while carrying could be a huge detriment to you is if you draw your weapon. It does not matter how justified you are in drawing and/or using your weapon - your accuracy will suffer, your judgement will not be as sharp, and your reaction time will be slower. In addition to these physical limitations, the resulting encounter with law enforcement is likely to be even more negative than it would be if you were completely sober.
Overall, I believe that there is no increased danger in carrying while drinking for those who have an accurate understanding of their inclinations and limitations - provided they do not draw their weapon. That said, I carry exclusively for self defense, and I would not fully trust myself to make the necessary critical decisions in a self-defense scenario if I had been drinking, so I would not personally carry a weapon while drinking. I certainly understand why some would choose to do so, and I do not condemn their decision. Each individual must make their own decision and be prepared to live with the repercussions that their decision may bring.