This is a weird and obscure tale, and one of my favorites. It appeared in Andrew Lang's Yellow Fairy Book in 1889, adapted from a tale of the Armenian people living in Transylvania and Bukovina. (Bukovina is a Central European region, which was once part of Moldavia and is now divided between Romania and Ukraine.)
In the story, a childless woman accidentally swallows an icicle, and gives birth to a little girl "as white as snow and as cold as ice," who can't bear any kind of heat. Then the same woman is struck by a flying spark from their fireplace, and gives birth to a boy "as red as fire, and as hot to touch." This is part of the widespread motif of pregnancy beginning with eating.
The siblings avoid each other as they grow up, since they can't bear each other's temperatures. But when their parents die, they decide to go out into the world. They wear thick fur coats so that they won't hurt each other, and they're very happy together.
Eventually, the Snow-daughter meets a king who falls in love with her and makes her his wife. He builds her a house of ice, and makes her brother a house surrounded by furnaces, so that they can both be comfortable.
One day, the king holds a feast. When the Fire-son arrives, he has now grown so hot that no one can bear to be in the same room as him. This is, as you might expect, kind of a mood-killer. The party is totally ruined. The king yells at the Fire-son, who responds by going full-on supervillain and incinerating him. The now-widowed Snow-daughter attacks the Fire-son. The siblings have a battle "the like of which had never been seen on earth," and which is left up to the reader's imagination. However, at its conclusion, the Snow-daughter melts like the icicle she came from, and the Fire-son burns out like a spark, leaving only cinders. And that's it.
I think it's interesting that snow is feminine here and fire masculine. This also not the only story about snow-related children. It's similar to the Russian "Snegurochka" (also known as "Snegurka" or "Snowflake"). There, a childless couple makes a snow sculpture which turns into a little girl. When she tries to play a game jumping over a fire, she melts away into mist.
This tale type, "The Snow Maiden" or Aarne-Thompson 703, has the moral that you can't escape your nature. The Snow Daughter and the Fire Son varies in that the fire is actually the snow-child's sibling.
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Researching folktales and fairies, with a focus on common tale types.