After a horse's owner is dead, is it still a crime to take his horse?

If the owner of a horse(NPC) dies, and is horse is roaming around, can you take it, or will it still be stealing?

If it is stealing, is there any way to make the horse yours if the original owner is dead?

Solution 1:

No, it will not be stealing (you can verify this by simply mousing over the horse - "steal horse" should not appear), and this "loss-of-ownership" has a tendency to happen a lot for random encounter NPCs such as "Hunter" and "Poacher".

The one caveat is that such a claimed horse, though it will show up whenever you fast travel, shows a blatant disregard towards you as a potential owner, and upon dismounting, will immediately set foot for where you originally found them.

"Wild" horses like this are irksome to keep track of, and usually its better to just shell out the 1,000 septims for a mount who won't snub you every time you stop to enter a cave.