The story is set in Iceland, inside a rough shewn log building with wooden benches along two walls, a wood throne on the third wall, two windows and a single door on the fourth wall.
Gunlöd, the daughter of Viking leader Thorfinn, stands quietly at an open window, and gazes out over the ocean. Valgerd, her mother, speaks about their shared grief over father Thorfinn's hard and unloving manner. In addition to the family's move from Sweden to Iceland, Gunlöd laments at having been forced to part with her dear childhood friend, the young man Gunnar, who has gone on Crusade in the Holy Land and who she has not seen in years.
Valgerd leaves the room and Gunnar unexpectedly enters, his ship having just arrived. Gunnar expresses his love and asks Gunlöd to return with him to Sweden. Gunlöd is coy but reveals that she secretly believes in the Christian god that her pagan father hates. Gunlöd is evidently torn between loyalty to her father, who is pagan, and her young Christian lover. Gunnar leaves the room before Valgerd returns, but says his ship will be waiting that night for her to make up her mind to go with him.
The night brings a terrible storm and with it Thorfinn's ship returns home from Norway. Thorfinn enters the house and in celebration he asks his daughter to drink from a horn of Odin, a pagan act. Gunlöd refuses, confessing that she is a Christian and not pagan. The proud Thorfinn is mortified and angry with his disloyal daughter. Meanwhile, a messenger enters and informs Thorfinn that a local council has banished him from Iceland for past deeds of theft and murder, he must leave at once or defend himself in combat. Thorfinn fights bravely outside the home while Gunlöd watches from the window. He defeats his enemies, but is mortally wounded and dies while seated on his throne surrounded by wife, daughter and Gunnar. Thorfinn's last words, "Eternal.. Creating.. God", show he has accepted the Christian religion and blessed the union of Gunlöd and Gunnar.

Question: Why does Gunlod refuse to drink from the Horn of Odin?
Answer: Gunlod refuses to drink from the Horn of Odin because she is a  Christian.
Alternative answer: she is Christian not pagan