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Bury a frozen-solid corpse into equally frozen-solid soil? 
Might be able to build a snowman on top of them at best, or waste precious time and resources on thawing the ground with fire first.
Not neccecarily.
There are quite a lot of reasons to start fires outdoors. And if you're starting them anyway, might as well use some to bury a corpse so you sleep better.
Especially since it's not actually the fuel that's soo precious, but the things matches / firestrikers required to start the fire. But, once you have a fire going, there's no waste in taking a brand from it, and a little bit of scrap sticks so you can dig a shallow grave.
And, besides, it probably wont even be neccecary to bury them at all.
Just drag the corpse with you, and scruffy, fluffy, and their raven friends will be happy to have a meal that they don't have to chase down first!
But, that's just a small detail, and stuff.