grew up on a 40 mile long lake that has one of the largest sturgeon populations in the world. At any given time in mid to late winter you'll have 300 fires going out on that lake with three stinky drunk dudes bundled up in blankets and Dickies jackets pulling 15 foot long fish out of the water. They're usually elevated to some degree-couple of good firepan designs out there, though none super packable. An old tin garbage can lid is about the best solution I've seen. It's often what we'll use on an unsupported whitewater kayak trip because it's the lightest and smallest thing to make one on when fires are restricted to a pan.
It actually doesn't melt as fast as you'd think, starting a fire directly on the ice. Water is a huge sink and on any body of water, you have lots of it.