Vietnam was slightly before my time. In the early '80s in Korea and as XO of a basic training company at Ft. Knox, I carried my own Series 70 Colt on occasion. One week, just before trainee payday, they withdrew all of our .45acp without replacing it immediately. This left the pay officers with M1911s and no ammunition for them. They gave us the choice of providing our own ammunition or carrying M16s. I carried my own .45 and my own very hot handloads using the 200gr. jacketed semi-wadcutter Hornadys.
In Korea, I carried my own .45 and had but didn't carry my Ithaca riotgun. A lieutenant in the next company over carried an 8 3/8" S&W Model 29. The year before I got there, that company had a patrol get pinned down in the DMZ by North Korean Light Infantry Brigade special forces. The battalion commander cracked and wouldn't send a relief force. He wouldn't allow our 4.2" section to fire illumination when the patrol ran out of 40mm illumination. In fact, he countermanded several attempts by a supporting 105mm unit to fire illumination, stating that he didn't want to create an "incident" if an illumination cannister landed in North Korea. The lieutenant ran into the TOC and asked the BN CO whether he was going to call out the quick reaction force. The col. replied, "What, me take THAT responsibility???" The lt. drew his .44 magnum and had to be dragged from the TOC before he shot the CO. A friend in the same company brought his 4" Model 13, but didn't carry it.
I taught the Korean security guards at our post to use their Winchester 1200 riot guns. I gave a demonstration of slam firing with my Ithaca. They were disappointed that their Winchesters couldn't do that.
I last put on a uniform in 1986, so I don't know what people are doing with personally owned weapons now.