I love games that don't hold my hand and encourage exploration. At first, I thought it was impossible to get through the area but then I tried going left and a whole new area opened up. I was able to get what I needed and returned to beat the game. The artwork is great and the music fits the icy cave really well.
A couple of suggestions:
1) Add animation to the player, even moving the entire sprite one pixel up and one pixel down will give him more life, and it will complement the foot sound effects.
2) Add the ability to play in full screen.
You definitely have a knack for level design, and I hope you keep making games!