Ah, that's very helpful @JustinB113 - thanks!
Not optimal to have the bath that close to the entrance of the palace, but it might be possible to add a story - like the palace was there first, then relation between king and his brother turned sour, brother sold land to a company starting a snow sports center. King and brother never spoke again after that, and now - 3 generations later there is still some hard feelings between descendants :)
My plan is to build the official ritual+meeting rooms in the middle hood, it seems to be the oldest hood and probably a tad more holy, too. Makes sense that some stately business takes place there. And if so, the palace up there in the snowy hood can be more secluded and entrance a little less impressive.
In another kingdom I was stupid to build private domains and throne room, offices and representation rooms on the same lot - it got way too massive for my computer and takes forever to load. So this time I will separate those businesses :)