I like these photos but it annoys me when someone goes to all the trouble to do such a shoot and mucks about with the weapons like some five-year-old.
That’s not a cavalry sword. And where’s the sheath? An unsheathed sword on a horse actually riding into battle is going to lead for a very bad time for you, the horse or most likely both.
The reason I mention that is of course the horse and the uniform though not of any particular army most closely resembles a Union Civil War cavalry officer’s as far as I can tell.
Most commonly soldiers would have their sword clasped between their left leg and the horse or immediately behind their left leg. Most people are right-handed so that’s the best place for it.
Still, even then it was mostly for show. Swords were used minimally if at all in the Civil War.