Grease behaves differently when it is cold
It sets harder and faster in a cold line than in a warm one. A kitchen drain that copes in July can start catching in January without anything else having changed.
Ground movement
Freeze and thaw cycles move soil, and soil movement can open a joint that was previously holding or worsen an existing belly.
More water going through the house
People are indoors, showering more, running the washing machine more, and hosting. Higher volume finds a marginal line faster.
Actual freezing is rarer than people think
Buried sewer lines sit below the frost line in most local properties. The exception is a shallow run or an unheated crawl space, which is worth knowing about before winter rather than during it.
The kitchen line specifically
Cold ground makes grease set faster and harder. A kitchen branch that has been marginal all year is most likely to fail in the coldest weeks, which is also when the house is busiest.
What to do about it before winter
If a line has given trouble in previous winters, dealing with it in autumn is considerably easier than dealing with it in February with guests in the house.
Holidays are part of it
A house with visitors puts several times its normal volume through the same pipe over a few days. A marginal line copes with ordinary use and fails under that, which is why the last week of December is reliably busy.
What is worth doing in autumn
If a line gave trouble last winter, dealing with it before the cold arrives is cheaper and considerably less disruptive than dealing with it during. The problem does not improve over the summer, it just stops being noticeable.