Tail carriage?

No - most horses will carry their tail higher when in motion like in your picture. They carry it higher when they are on alert or excited typically also. It's not an indicator of "happiness" per se. Having said that, a very frightened horse will usually tuck its tail and an agitated horse will flick it from side to side. So if your horse holds its tail up like that in general, it's probably at least not very nervous.
 
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