Here are some story ideas using the character Snowman, prop of a Mirror. and location of a Castle.
1. An adventure story of a child hero character going to a icy castle to stop an evil snowman, brain washed by his cursed hat, with a magical hand mirror in a similar manner to the greek myth of Perseus and Medusa however instead of the snowman turning into stone, the power of the hat fades away and he's back to being a friendly and kind snowman.
2. A unlikely romance between two snowpeople, one is a princess and the other is a peasant working in making mirrors from ice. The snowman is a mirror maker, and as he carries some of his stock through the icy woods near the snow castle, he comes across a clearing with a pond in there, shocked to see the princess there in tears. In an attempt to comfort her, he gives her a mirror and they talk for a while. After a date montage of the different places they go, they head to the castle on their last date where they dance, the shot being shown through the mirror the snowman gave her.
3. Snowman made by a child gets jealous of an ice sculpture made by a eccentric artist. Envious the snowman looks at his reflection, hating what he sees. He begins to dream of an alternate life of him being rich, successful and happy, living in a big snow castle and being able to get anyone he wants. However he then sees his creator, the small child and realises that this dream he has isn't worth it because thats not what the child wanted. He learns to be happy with himself because his purpose of being created was to make the child happy.
4. Prince builds a snowman, who is able to move and talk from the magical scarf the boy puts on him. The child is over the moon and leads the snowman inside the castle, where the snow creature then processed to cause icy havoc for the staff and the king himself. The prince is upset over the snowman's actions and sends him away. At the end the snowman either realises his mistakes and from that the magic cause him to transform into a human or he meets the child once again and gives the child back the scarf figuring that thats probably for the best if he was just a normal snowman.