Ash is a pretty good insulator so it might be able to run over ice - for a while anyway. Eventually it would eat through, assuming the lava kept coming but a layer of cooled lava would form at the base (so it would be rock (mountain), ice, ash, rock (cooled lava), lava - then the lava would cool from the top down too). I think it makes more sense for the lava to follow the melt water channels. it could then make lava tubes below the ice - they'd keep the lava hot as it is insulated from the outside inside its tube. There's a lot of stuff in that link - I'm to tired to make heads or tails of it tonight. I shall take a look tomorrow.