The snow would melt but the fire could still burn on top of the melt water the materials that are burning may have also melted so not be clearly visible as chunks (if it was some kind of oil based solid, inflammable polymer something like that).

The ice underneath could refreeze some of the melt water (there is a lot of ice there) so we might not be talking about an instant lake just a puddle with flames on top until the fuel runs out.

It might be fun if the impact set off an avalanche which the droid speeds away from.

Now that would put the flames out.