A solid entry with good use of the theme! I encountered a bug where I was stuck on a piece of ice, so I had to reload. Maybe you could add a restart button?
Also, there is some strange glitch with the graphics. Whenever I move, lines appear on the screen.
Overall, the game needs some additional polishing here and there.
Viewing post in Cavern of Ice and Fire jam comments
Restart button is a good idea. I don't know if you were aware of it but there is a pause screen (press Esc), which allows you to go back to the main menu and then load any level from the level select.
I had the graphical issue occasionally, but nowhere near as bad as you are describing. I think it is related to Unity's tiling system. Unfortunately, I do not know how to fix it and didn't have the time left to figure it out.