I've never seen a horse wag it's tail as such, I've seen them swish to get rid of flies and sometimes to show irritation if they also have their ears back, but nevr happily wagging like a dog.
If a horse is swishing its tail and its not a fly flick then beware, its getting wound up about something. I used to ride a beautiful grey. If I got things right he would relax in tail and ears, if I got things wrong, he would swish his tail.
Ears forward and alert yes relaxed and all well - but that's not happy like a dog who wags and cats that purr. I find horses very lacking in warm demonstrations of feeling recognisable by humans.
They don't wag tails or purr, but they are very affectionate to people they know and like and whicker when they see you. I think anyone with horses can have am accurate guess at how they feel at any point.