Really intriguing and creative take on generosity, really love the real-world impact you've considered.
Unfortunately I had a similar issue to others, that "IJKL" didn't seem to do anything - sometimes my little critter would catch up, sometimes it'd just struggle in the snow so pressing the buttons was a gamble and I had to release and press again many times to try see if it would work that time. Picking up embers and all that was intuitive and I love love love the atmosphere you've created with how nicely the golden light burns away the cold creeping into the screen. The simple soundtrack also adds to the desolation of the area and generally you just nailed the atmosphere and visual. I also didn't have a clear idea of where I was meant to go next, resolving to try get the critter back to the first camp fire proved too difficult since the IJKL keys don't provide their desired effect.
One thing I'd like to see would be the player physically carrying the creatures, possibly travelling slower with more critters attached. This would also be a great indicator of the permanent button press working since there's a significant difference between press (critter climbs onto player) and release (critter gets off/falls off). A visual indicator of how much time the player has before a companion freezes beyond saving (i.e. they would "shrivel up" and start laying down) would also add some context and desperation to the situation.
I do absolutely love the concept and I hope to see a full version of this!