Iceland competed at the 1956 Winter Olympics in Cortina d'Ampezzo, Italy. This was the first time Iceland sent a woman to compete in the Winter Olympics.
Alpine skiing
Men
AthleteEventRace 1Race 2TotalTimeRankTimeRankTimeRankSteinþór JakobssonGiant SlalomDSQ–Stefán Kristjánsson3:59.162Einar Kristjánsson3:53.460Eysteinn Þórðarson3:49.456Stefán KristjánssonSlalomDSQ–––DSQ–Einar Kristjánsson1:50.0362:28.6404:18.637Eysteinn Þórðarson1:44.7302:15.6294:00.326
Women
AthleteEventRace 1Race 2TotalTimeRankTimeRankTimeRankJakobína JakobsdóttirDownhill1:57.231Jakobína JakobsdóttirGiant Slalom2:39.441Jakobína JakobsdóttirSlalom1:06.423DSQ–DSQ–
Cross-country skiing
Men EventAthleteRaceTimeRank15 kmOddur Pétursson1'02:3661Jón Kristjánsson58:235530 kmOddur Pétursson2'10:1648Jón Kristjánsson2'00:5239
References
Sources Official Olympic Reports Olympic Winter Games 1956, full results by sports-reference.com