Talk to the Queen of Snow to begin. Ask if she has a task for you. She explains that she and the Queen of Sunrise are fighting for the Year using evil trees. She then explains that the Queen of Sunrise is guaranteed to win. Then, she asks the player to chop down an evil hawthorn tree to damage the Queen of Sunrise's offence, and says that she will give the player an Icicle crown for helping her.
To do this, find the current evil hawthorn tree in the Hawthorn area. If it is fully grown, you can chop it, but if it is not fully grown, nurture it until it is. Once you have interacted with the evil tree (or its roots) at least once by either nurturing or chopping, and it falls (i.e., dies) you will get a confirmation message that you have defeated an evil hawthorn tree. Go back and talk to the Queen of Snow.
The Queen of Snow will say that she sensed that you had killed an evil hawthorn tree. She will thank you for fighting for her. She will then give you the Icicle crown. Quest complete!