In Ultima V you can leave your horse by hitching-posts in towns to prevent them from wandering away but it appears that if you don't retrieve horses before night they always get stolen! (horse is no longer by the post) Is there some way to rest in Inns overnight without losing your horse?

You are correct. I discovered that you can safely leave your horse on the world-map so apparently the hitching-posts are useless.

Yeah. One of those occasions where the attempt at immersion was noble, but the engine wasn't able to handle it properly. I lost a horse in Castle Britannia back in the day - and I'd spent all my gold on the bastard too.

Another example was in Ultima VI...

The entrance to an inn has a sign telling you that weapons aren't allowed in here and please leave all weapons on the tables.

I dutifully stacked all my weapons on the tables so as not to cause trouble.

But when I was finished with all tavern conversations and quests and went to pick up my weapons, only the first in the stack were available. My other 15 or so weapons that I'd bought/collected throughout the game had disappeared.

There was only one save slot and I'd saved inside the tavern so I was screwed. That's when I stopped playing and didn't start again for many years.