Basically, it's a multi-tiered fountain, built on the conventional bowls-of-increasing size model, but with one crucial difference: every second tier spills out a curtain of ice chips rather than water.
Rather than cooling and warming the respective tiers, the fountain is actually two fountains
in one - one which uses ice, and one which uses water. In the centre of the fountain is an archimedes screw with a hollow centre - water is pumped up the hollow centre (to emerge from the top of the fountain in the obligatory plume), while the rotating screw churns the ice chips upwards from a hidden tank at the base of the fountain. The water collects underneath the plume in a small basin which overflows into the next, slightly larger basin beneath. Now - here's where the ice chips come in (and where the idea gets kind of hard to explain): although the next tier looks like a single bowl from ground level, it's actually comprised of two concentric bowls - an inner one which catches the water and filters it down to the next level, and an outer one into which the ice chips are being churned. In the outer channel are rotating paddles which push the chips over the edge of the bowl and into the next tier. As the paddles revolves they also create an interesting helical cascade effect in the falling ice curtain.
On the next tier, the arrangement is reversed, with the inner channel catching the ice chips and taking them down (through the unseen insides of the fountain) to the next tier, while the water from the tier above flows through the fountain into the outer channel.
Repeat as desired.
The bottom tier is - in true fountain style - a big pool of water, with all the ice chips falling unseen into a tank below the pool which filters it back into the screw so they can begin their journey all over again. At least, that's the simplest option. But there could be variations on this...
Originally I envisaged the final tier as having a series of lips (like the lip on a jug), alternately gushing water and ice into the pool below. It would have little flames burning from the edge of the bowl inbetween the lips. But then it would be too hard to recover the ice chips (unless anyone else has any ideas..? Silly question).
I also toyed with the idea of both the water and the ice chips returning to separate tanks underneath the fountain, and the final tier spilling dry ice smoke into a large pool beneath it. Again, bit tricky to do in real life - especially if there's a strong wind a-blowin.
Sorry if this idea's a bit badly explained; a diagram would probably help. I did try drawing one, but it only confused me all the more. It all works perfectly in my head, though.