I did some testing to figure it out, so I could get it right on the guide:
Here's a shot with both a cat and dog ghost. After adopting some elders and sending them to meet Grim, I think I have it figured out. Unicorns/Horses are red, while dogs and cats will go either red or blue upon death. They then seem to stay that color.
It is as you say, and they cannot drown. The dog I tried to drown actually teleported out of the pool automatically. It seems they are really coded to die only of natural causes. The few times I have had meteors since this EP they were all centered on my Sim. With my animal slots usually full that means it's really unlikely the game would ever target them.
I am glad it's random for the dogs/cats. Personally, I prefer the blue ghosts.