I'm probably going to run a Rime Western game here as play-by-post (with the spiffy name of 'The Rime: A Frostpunk Western RPG'), because the idea continues to roll around in the back of my head. Now, it's my own spin on the concept, but it retains the 'steadily expanding frontier', 'grim people in heavy coats fumbling for their revolvers with frostbitten fingers' core aspects, at least. The world's not an ice sheet, but rather simply covered by an icy and seemingly endless black sea. The sea level is continually falling, revealing ever more land to be settled - but this land is so cold from the embrace of the sea it can't sustain any crops for at least a generation. As the seas recede and the edge of the frontier moves out, these lands gradually warm up and nature spreads in from inland.
So, we get a frontier of ice and snow, and a nifty reason for settlers to be coming here (claiming land that will be worthwhile if you just hang on long enough), but we still get an inner region of the world that produces industry, food and city slickers.
The sea's not entirely lifeless, though. Edible kelp, hardy sea creatures and native Mer have existed there quite fine for millennia. The Mer (your basic aquatic humanoid people) are faced with losing their homes to the merciless growth of land. They can move deeper to rebuild or try to live on land (where they survive alright, when they can regularly access water). Some have taken to attacking human settlers, figuring they're to blame for the sea levels falling. There's some pretty obvious parallels to real history here, I realize now. Sea cattle are an important food source, too - ranchers drive herds of 'em up and down the edges of the Rime and through artificial canals inland to be slaughtered.
There's all kinds of stuff I want to do here, but that'll wait for the game. Mechanically, I'll handle things with a d20 system. Things are intended to be pretty brutal and unforgiving. Characters will die without a heat source at night. Combat very easily kills, so you'll want to be the first one to draw and fire. There's no HP system, but rather Wound levels, where attack rolls can result in glancing hits, wounds, severe wounds or death depending on degrees of success. There's some things to offset this, so the game's not outright murderous towards the players, but I feel it's a good way of representing the harshness of life in the Rime.
The physics or metaphysics of the world raise a lot of questions, sure, but I've tried to make something internally consistent. It's an alternative world, so it's all good.