My first critique is that your ice doesn't really look like ice, more like metal. I realise you didn't design the sprite but you could definitely improve the effect of the ice version by introducing some darker "transparent" spots and rim lighting. Here's an animation of an frozen character I did a while back that shows what I mean and might serve as some inspiration:
In animation terms I think you would be well served by increasing the number of frames. I think even just one more would really help since they're quite jerky when you loop back. On the hair for the normal guy I'd suggest having the flick point downwards on one frame as he rises and then flip back up. Right now you have two frames exactly the same and that really kills the animation. Same for the head motion in general, you want to try your hardest to keep it always moving. I would also say that his arms and particularly shoulders rise up a bit too much. The fire in the animation looks too solid, the key to a good fire is that parts of it will have to come off the top and dissolve, as the flame "whips" the tip of it could break off for example.
I think if there's one thing that would really help you it would be to take all of the parts individually and decide what their cycle is, the head for example moves in a circle, the body moves up and down etc. And make each of those cycles looks as smooth as possible. If you get each individual part right it should all come together into a nice animation.
Anyway I like the designs and concepts, the spinning ice magic is very cool
Good luck with these. Also you should post them at 1x zoom to make editing of them easier.