In contrast, World Cup winner Manie Libbok had a nightmare evening with the boot missing all his kicks at goal in the wet and windy conditions.
Player-of-the-match Horne told BBC Scotland: "We've got the benefit of having this [weather] all year. We do a lot of work on it, kicking into the wind, so I'm chuffed.
"They're an unbelievable team, so physical. Our big men up front were unbelievable. They stood up to every test. The Stormers were battering at the door and we held them out. Credit to everyone.
"As a group, we've not been great at this year - when the going gets tough we've gone into our shells. Sione Tuipulotu was barging down doors, Seba [Cancelliere] doing what he does, and that was a huge moment for us. I'm glad they're on our team.
"It's a massive challenge, they're a class team and they're the reigning champions for a reason. If we front up like we did tonight, why can't we?"