Cool-season lawns: why then
Keep mowing as long as the grass keeps growing — usually until a couple of weeks after the first frost. Take the final cut slightly shorter than summer height (never scalped): shorter winter turf mats less under snow and resists snow mold. Leaves must be mulched or removed before snow regardless.
Warm-season lawns: why then
Warm-season growth slows sharply as nights cool and stops when frost sends the lawn into dormancy — typically within two weeks of the first frost, after which the lawn browns and mowing is done for the year. In frost-free areas growth merely slows, and occasional winter mowing continues.