After Scotland's failure to overturn the two week ban that their first-choice number ten Finn Russell received for his disputed challenge on Dan Biggar in their 26-23 home defeat against Wales two weeks ago, Horne has been chosen to replace his Glasgow club-mate in the pivotal position.
At 92 kg, 14st 6lb, Horne is not exactly a flyweight fly-half but the 25-year-old - who has played most of his rugby as an inside-centre - will be up against a monster of an opposite number in the 113kg, 17st 13lb form of the New Zealand-born Haimona.
"Peter played well in his last two outings for Glasgow at first-five [outside-half] and he controlled the play," said Cotter, who will be seeking his first Six Nations win following defeats against France and Wales. "He offers another profile and we are all backing him.
"This is a big year of rugby and it's going to be an important game for Peter and for us. Without applying too much pressure on him, he knows that."
Horne, who will be making his seventh appearance for his country but his first on home ground, insisted that he was undaunted by the prospect of facing Haimona, who made an impressive debut against Samoa in November - kicking 14 points in a 24-13 win - but whose form has been patchy in Italy's Six Nations defeats at home to Ireland and away to England.
"Yeah, he's a big fella," said Horne, "but I think in the majority of my career I have never been a biggest guy, so it's something I am used to.
"I will look forward to that physical battle and making sure I get stuck into him and not give him any gain line. We'll see how it goes."
Scotland - who also have Tommy Seymour back on the right wing, Euan Murray returning at tighthead prop and Tim Swinson replacing the injured Richie Gray at lock - are under pressure to produce a victory after pressing both France and Wales close.
The Scots are on a run of four successive home defeats in the Six Nations, their worst in the championship since 1977-79. A fifth defeat would be their longest losing streak since the dark days of 1951-54, when they lost seven championship games in a row at Murrayfield.
Italy have not won in the Six Nations, home or away, since a 22-15 success against Ireland in Rome on the last day of the 2013 championship.
Their only Six Nations triumph on the road came at Murrayfield in 2007, when they plundered three tries in the opening six minutes en route to a 37-17 victory.
Italy's head coach Jacques Brunel has made six changes but kept faith in Haimona, who was influential in the Azzurri's outstanding opening quarter against England two weeks ago but missed all four of his kicks at goal.
"Kelly showed good things at Twickenham," said Brunel. "We have to trust him. We need continuity in a key role."
Brunel described Scotland as a vastly improved team with "no major weaknesses."
"It's going to be a difficult game but I expect a lot more from my team," he added. Cotter described Italy as "a better team" than they were in 2013, when they beat France and Ireland.
"It's a great test for us," he said. "We saw what Italy did to the Irish forward pack; I thought they knocked them around.
"They scored three tries against the English at Twickenham. These things did not go unnoticed. We're preparing very seriously for this game."