Horne produced a nerveless display against the Ospreys last weekend to convert two late penalties and stretch Glasgow's lead at the top of the PRO12 table to four points, a performance that put him firmly in the Scotland spotlight.
The Warriors No.10 has amassed 60 points in his 14 league appearances so far in a successful season, including two tries in this month's 54-10 win over Zebre.
And Cotter hopes Horne can provide a similar return against Italian opposition this weekend when he replaces club-mate Finn Russell to preserve an almost complete Glasgow back-line against Italy.
"Peter gets the nod through his experience and through his recent games at Glasgow," Cotter said.
"We think he controlled those games well and that gave him the nod just ahead of Greig (Tonks, of Edinburgh Rugby).
"He's very excited about the opportunity to play at ten. He has played with those players who will be outside him.
"We know what Greig can give us coming off the bench and that is flexibility at ten and 15. It's nice to have somebody who can do those roles."
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