Rose go into the match looking to bounce back from Saturday’s 5-2 to loss to Rangers B which ended their run of eight straight wins.
The defeat, before a bumper crowd of 942, left Rose just one point clear of the Ibrox Colts, who have two games in hand, at the top of the Lowland League.
"I thought we let ourselves down a little bit and I can't really say that about our players very often," said Horn, whose side were chasing an Old Firm double after beating Celtic B on the opening day of the season.
"We probably showed them a wee bit too much respect at times and I don't think we were physical enough with them.
"You've just got to move on, forget about it.
"The Scottish Cup is massive for the football club. We're expecting a really tough game up there. No matter who you play from the Highland League they make it difficult for you.
"They're in your face and up for the challenge and we've got to be ready for that."Hopefully, if we can match that, our quality can come through."
Rose are one of four Midlothian team in Scottish Cup action on Saturday.
Penicuik Athletic host familiar foes in East of Scotland Premier title rivals Tranent – the two sides are locked together at the top of the table with 10 wins from 11 games.
Cuikie enjoyed a remarkable 11-2 win over Hawick RAU last weekend – and gaffer Stevie McLeish reckoned it could have been more.
He said: “The first 20 minutes we were well within ourselves. Suddenly they score a goal and we pick ourselves up a bit. After that, we were absolutely relentless.
"We scored 11 but we must have missed another 11 or 12.”
Dalkeith Thistle, having come through their first-ever Scottish Cup tie in the preliminary round, have a tough test away to West Premier title contenders Clydebank.
Newtongrange Star will also be underdogs at home to a Dalbeattie Star side going well in the Lowland League.
However, Nitten’s opponents were on the wrong end of a cup upset last week when they lost at home to Whitletts in the South Challenge Cup.
It’s a big weekend of cup action at New Victoria Park with the Newtongrange youngsters also in action on Friday night against St Mirren in the first round of the Scottish Youth Cup.
Tickets for both games are available from the club website.