A very powerful story written by a "new" writer at the time in a collection of short stories sometime in the 70s. A mother and daughter (named Saura) live in a cabin and discuss going further South where it is colder. They are helped by some guy on a horse who protects them but is ultimately killed by some intruders. The mother determines they will go where it is "warmer" if they are left alive but the feeling I recall is there is really not a place warmer. Kind of like The Road.
This appears to be "The House By the Crab Apple Tree" by S.S. Johnson, 1964
The Best from Fantasy and Science Fiction. Anthony Boucher (editor) Little, Brown, 1965
The Best from Fantasy and Science Fiction: 14th Series (The Best From Fantasy and Science Fiction #14) by Avram Davidson
She could hear her mother scream long ago as that gang used her for their purposes. Saura wanted to run and help her, but she remained hidden and safe. She took a step toward where ... The bed was warm and Saura shivered comfortably.
She shrugged and turned to the stove and replaced a lid that had been kicked out when Verie fell. Then she opened the oven door, reached in, and ... Saura nodded. "That was Weed." "What happened?" Saura quietly told how the men had come after Weed had left for wood, and what had happened until the time that Ted had stepped inside and shot King. "Shall I bring him in until we can bury him?"
Also in The War Book by James Sallis, 1971