Kirstoff was referred by many as the Mountain Man, but I personally would like to call him an ice merchant, because that was his business, selling ice.
Anyway, he was first seen at the beginning of the story as a young child with a young reindeer, learning how to draw ice from the mountains, until the found the king and the queen rushing towards the place of the trolls, where they asked help in melting the frozen head of Anna. They were soon adopted by the group of trolls.
Later in the story, Anna and Kristoff met at the "Wandering Oaken's Trading Post". In exchange for Sven's carrots and other stuffs, Anna asked Kristoff to take her to the North Mountain to search for her sister Elsa. On the way, they had an ncounter with wolves, Elsa's marshmallow ice monster, and met Olaf.
He rushed Anna to the trolls when he discovered that Elsa struck Anna's heart. Upon learning that only an act of true love can save Anna, they rushed Anna back to Arendelle's castle so she can be with Hans. But when he saw a snow storm coming towards the castle he went back to save Anna.