Following trips to Forres Mechanics and East Stirlingshire, Rose were handed an away day for the third round running when Sunday’s draw paired them with the cinch League 1 outfit.
Alloa will start as odds-on favourites – but that doesn’t bother the Bonnyrigg boss.
He said: “It's a really tough tie, again we could have got a lot easier.
"Since getting relegated from the Championship Alloa have had a wee bit of an indifferent start to the season but they had a really good result against Queen's Park.
"Barry Ferguson is a winner and will have them organised and fired up. But it's a free hit for us, we go through there with no fear.
"We've beaten teams in League 1 before, we've beaten Dumbarton as a Championship team and taken Dundee to extra-time so we look forward to the game."
Horn was delighted with Saturday’s second round win over Shire, goals by Kerr Young, Bradley Barrett and George Hunter securing their 3-0 victory.
He said: “It was a great win and a really good team performance. We scored some good goals and it could have been more to be honest, the way we played, and we're delighted to get through to the next round.
"At half-time [leading 2-0] we said go and get another goal and really kill it off. It didn't come until a wee bit later in the game than we would have liked but we still looked the more likely team to score, we still created opportunities.
"It was a big game, East Stirling have been going well this season and we looked at it as a really difficult tie. But the way we played made it easier than I thought it was going to be."
Rose’s cup commitments go on the back burner as they return to Lowland League duty this Saturday with a home match against Civil Service Strollers, one of only two teams to beat Horn’s league leaders this season.
Horn said: “Civil Service Strollers are going really well and had a great result themselves in the cup on Saturday. They're a good side and Gary Jardine's got them well organised and they're got really good players there.
"They turned us over at the start of the season so we'll be looking to avenge that.”