Hi there!
I wonder which content you pulled this from? Very tricky stuff, first time I ever saw it! Had to do some searching, but it looks like it’s a saying (속담) - which has basically no relationship to “You can lead a horse to water…”
The correct phrase is “평안감사도 저 싫으면 그만(이다).”
평안 is 평안도 (平安道) Pyeongan-do, or Pyeongan Province, modern day North Korea (now it’s split into North and South Pyeongan, apparently). In the Joseon Dynasty, Pyeongyang was indeed the provincial capital of Pyeongan Province, so the mistake in your quote is reasonable and apparently common. In this case 감사 is not the 감사 we all know, but 감사 (監司), a kind of 2nd level government official in the Joseon dynasty. A provincial governor, basically. (Thus 평양 is a mistake. You can’t be the provincial governor of a city; only of a province. Naturally, I guess modern people have forgotten what a 감사[監司] is.)
The northwest area (including 평양) was really important historically on the Korean peninsula: around 100 BCE it was the capital of the ancient 고조선 kingdom, for example. By the end of the Joseon dynasty, when this saying comes from, the area was really wealthy, with lots of merchants and good education. It seems like people at that time could consider 평안도 the 2nd most important place in Korea after the Seoul area (which was the capital of Joseon). So if you were the governor of such a place, that’d be quite the responsibility/honor!
So this little 속담 is a kind of hyperbole - “Even if you become the governor of 평안도, it’s no good unless you like it”. Korean websites usually gloss this as something like “No matter how good something is, it’s useless if you don’t like it.” or “No matter how good something is, it’s difficult to do it against your will/desire.”
At least, that’s what I can understand from doing some searching. Here are some websites explaining this: here and here
(According to the first one, apparently this old saying is gaining in popularity online recently. According to the 2nd, it’s very common that people mistakenly write “평양”, like in your example.)
Another gloss is found here: this just explains it as “No matter how good something is, you can’t force (yourself to do?) it if you don’t like it.”
These are the kind of Korean learning moments where you kinda lament the fall of hanja in daily use. Then there’d be no confusing 감사 with some other 감사 with some other 감사… Of course, it’d make our learning of Korean much harder, but it’d also make the auto translation resources we have much more effective