“Saddled” isn’t an ability that a creature has. It’s just something true about that creature. It won’t stop being saddled until the turn ends or it leaves the battlefield.

You may activate a permanent’s saddle ability even if that permanent is already saddled.

“Saddle N” means “Tap any number of other untapped creatures you control with total power N or greater: This permanent becomes saddled until end of turn. Activate only as a sorcery.”

If a permanent becomes a copy of a saddled Mount, the copy won’t be saddled.

Creatures with saddle can attack or block as normal even if they aren’t saddled.

An ability that triggers when a creature “attacks while saddled” will trigger only if that creature was saddled when it was declared as an attacker.