The Flaming Ice Picture
First off, let's talk about the Wordless Wednesday photograph. I am guessing it was created using Photoshop, but you can get the appearance of burning ice very easily. Get some glass cubes (craft stores carry them), set them on a surface that can withstand fire (metal pan, pyrex, stoneware), pour something flammable over the 'ice', and set it alight. You can use 151 rum (ethanol), rubbing alcohol (try for 90% isopropyl alcohol, not the 70% alcohol stuff), or methanol (Heet™ fuel treatment from the automotive section of a store). These easy-to-obtain fuels burn cleanly, so they won't set off your smoke alarm (I know... I tried). If you want colored flames, you can add any of the usual flame colorants to the ethanol or rubbing alcohol. If you use methanol, try adding a little boric acid for a brilliant green flame. Use caution with methanol, since it burns very hot. One little display tip: You can give glass cubes the imperfect, crackled appearance of water ice by setting one on fire and then tossing it (with tongs) into water after the fire goes out. The glass may shatter, but if you have the temperature just right you'll just create internal fractures that look very pretty in photographs.
I basically told you how to set ice on fire last week when I told you how to make a flaming B-52. High-proof ethanol (like 151 rum) or 90% isopropyl alcohol will float on the surface of water and mix with it so that as long as there is fuel, your ice will appear to burn. Don't use methanol... as the ice melts, it will extinguish the flame. You can use ethanol on ice used for human consumption (or flaming ice cream drinks). Rubbing alcohol is toxic and should only be used for decorative purposes.
Really Burning the Ice
You may be thinking it is impossible to burn ice. Strictly speaking, that is not true. You can burn ice, just not water ice. If you make ice cubes from any of the alcohols I have listed, you can burn them. For pure alcohol ice cubes, you'll need a way to freeze the liquid down to about -100°C, give or take a few degrees depending on the specific alcohol. You don't need to get quite that cold for 75% alcohol/25% water ice, which will burn if you spritz it with a little liquid alcohol to get flammable vapor over the ice. You may be able to freeze the 75% solution over dry ice.
These photos were taken myself, indoors, right under my smoke alarm. I did set the alarm off once when I got too enthusiastic with the rubbing alcohol. It was a challenge to take a reasonably focused picture in dim light, but the project itself was easy to perform. Just remember two things: (1) If you want to ingest the flaming ice, only use food-grade ethanol, not some other fuel. (2) Methanol burns very, very hot! You can get away with using almost any surface if you use ethanol or isopropanol (hey... you can even touch the flame briefly). The uncontrolled-fire and burn risks are much higher using methanol because it produces so much heat.
Enjoy the project, whichever version you use. Have fun!