This is actually quite good! The jumping feels nice and controls well, the dynamic camera & its movement is a pretty slick thing, and even the sprite changes to reflect status are a nice touch!
My only 2 complaints are 1. how despite having a health bar, everything still kills you in one hit, and 2. how you never really worry about running out of health, since most ice cubes are hard or impossible not to collect, and so you're usually recovering health faster than you can lose it.
If you make it so that spikes just deal damage (maybe 1/4th your health bar?) instead of killing instantly, that would solve both these issues at once ;) Then there'll be pretty much no problems here! ^^ (aside from the occasional unimportant visual goof)