I can confirm that the random planets seem biased in favour of low density ice (~2.3) It does melt, however, it just takes a little while. Proportions of 40 - 50% water by mass are quite common.
However, in a quick and dirty sim, they all melt, as does a 100% water ice object (which ends up as existing solely as plasma but takes on its original terrain map. In this case it was built off Mars, so it becomes mars.)