Olaf's relationships with the other characters of Frozen. A self-proclaimed "love expert", Olaf was friendly to everyone he encountered and, despite his naive innocence, had a profound impact on others.
Allies
Anna
Though Anna was weakened by both Elsa's curse and Hans' betrayal, her spirits were lifted by Olaf.
Olaf met Anna while she was traveling through an ice forest. He agreed with her comment about the beauty of winter and revealed his presence, unaware that his sentience would startle her. However, in spite of losing his head to Anna's instinctive reaction, Olaf bore the princess no ill feelings and warmed up to her after she helped realign his head and presented him with a carrot nose. The snowman grew eager to help Anna on her quest upon discovering that her mission was to restore summer. The two of them were of similar mindsets, expressing optimism with regards to Elsa thawing the winter.
As their journey continued, Olaf and Anna grew close, particularly when they combined their efforts to persuade Elsa to return to Arendelle. On multiple occasions, Olaf displayed a willingness to ensure Anna's safety, even volunteering to stand up against the hulking Marshmallow to provide her time to escape. The snowman was also especially concerned when he found Anna lying on the library floor and hastened to start a fire, at personal cost, to keep her warm. When Anna expressed disillusionment over Hans' betrayal, Olaf lifted her spirits by teaching her what love really was; he also helped Anna realize Kristoff's affection for her.
Devastated upon realizing that Anna had succumbed to her curse and froze solid, Olaf expressed both surprise and joy when the princess thawed out. Though the snowman was initially unsure of how Anna recovered, he ultimately deduced that her sacrifice to save Elsa constituted an act of true love, thawing her frozen heart.
After summer returned to Arendelle, Olaf helped Anna maintain her balance while skating in the courtyard.
Elsa
Olaf was built and given life by Elsa.
Despite his limited interaction with Elsa, Olaf had a natural affinity for his creator, able to confidently lead Anna to her location. Olaf also cared for Elsa immensely, expressing faith that she was a nice, gentle and warm person before even meeting her. However, his first encounter with Elsa did not go as intended; though Olaf and Anna reminded Elsa of her happy childhood, she remained fearful of her powers and created Marshmallow to throw the snowman and her sister out.
Olaf encountered Elsa again in Arendelle, where he mourned with her over Anna's sacrifice. However, he also shared in Elsa's joy when the princess was revived and helped Elsa realize that the key to controlling her powers was love. When Elsa used this knowledge to restore summer to Arendelle, Olaf began to melt in the heat but was quickly restored by his creator, who also gave him a personal flurry to stay cool.
Olaf later joined Elsa on the ice rink she created, helping her to teach Anna how to skate.
Kristoff
Olaf and Kristoff seem to have a good friendship, and care about each other. When they first meet in the forest, Kristoff (like Anna) was at first frightened by the living piece of snow, but later became accustom to Olaf. When Olaf tells of his desire to experience summer, Kristoff was intentionally going to tell the snowman that he would melt in the heat, but Anna stops him from ruining the living snowman's dream. He still believes someone has to tell Olaf, but doesn't proceed to do so himself. When Elsa created Marshmallow to throw Olaf, Kristoff and Anna out of the ice palace (to ensure she doesn't accidentally hurt them again), Olaf tells Kristoff and Anna to run, and tries to distract Marshmallow for them, but is unable to do so when he was thrown out piece by piece. When Kristoff and Anna were dangling from the cliff, Olaf tried to stop Marshmallow from attacking them. Once at the bottom of the cliff, Olaf asked Kristoff to help him retrieve his lower body parts, which the ice harvester did. Once they reached the Valley of the Living Rock, Olaf thought Kristoff was crazy because he was talking to what appeared to be rocks, but then learnt that the "rocks" were Kristoff's troll family (and then learnt that his name was Kristoff, because Olaf thought his name was Sven the whole time). On their way back to the castle, Kristoff told Olaf to stay out of sight (probably for fear that the other citizens would be scared of and try to harm the living snowman). While he was helping a dying Anna stay warm, Olaf revealed to her that Kristoff loved her while telling her what love truly is, showing that Olaf and Kristoff were close enough for the snowman to understand the ice harvester's feelings. At the end of the movie, Olaf and Kristoff celebrate on the newly created ice rink with all their friends.