It has been done before and the gentleman below has made wonderful sounds out of it last year. While skating on thin ice (less than 2 inches thick) he seems to have been able to control the movements for some great sound. Not long ago (a matter of hours really) someone tried it in Norway the results from the Australian newspaper are at this link. The skater below really has taken it to another level. However the ice that is this thin can be hazardous and is not recommended. It also has a lot to do with the ice thickness and the lake's dimensions as described in the report. Nature does some great stuff. Meanwhile another guy discovers skip rocks across a frozen lake can make great sounds too. Witness.
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