“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.

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

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

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

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.