The actor, who has only recently graduated from drama school, will star in the show's forthcoming Christmas special.
He told the Ilkley Gazette: "I finished the Central School of Speech and Drama on the Friday, had the audition on the Monday and by Thursday I was filming in Cardiff."
He added: "I was very excited about the audition but didn't think I'd get it. It took a month to film and I've been up and down to Cardiff. It's a relatively good part."
Horn's role in the episode is currently unknown, though he confirmed that he had spent most of his time on set with guest star Katherine Jenkins.
"We were together for a lot of the episode," he explained. "Let's just say I might be a bit of a hero with the boys."
He also praised fellow guest actor Michael Gamon and series star Matt Smith.
"Working with Michael was fantastic as he's one of my heroes, and Matt is brilliant to work with," he said. "[He's] absolutely fantastic."
The currently untitled Doctor Who special will air this Christmas on BBC One.