Hair (머리카락, meori-karak) is generally read as a stand-in for vitality, pride, or status — long, healthy, well-kept hair reflects the same qualities back onto the dreamer's current circumstances, while damaged or thinning hair reflects the opposite.
Cutting your own hair deliberately, especially if it feels freeing rather than upsetting in the dream, is read as shedding old worries or making room for a fresh start — the same purifying logic found in a snow or rain dream elsewhere on this site, applied to your own body instead of the weather.
Hair falling out unintentionally, as opposed to being cut on purpose, is read quite differently — as stress, worry, or a loss of vitality or standing, generally read as a warning worth paying attention to rather than a positive clearing-out.
Someone else cutting or styling your hair without your full control over the outcome is read as being influenced or changed by another person's decisions right now, for better or worse depending on how the result actually looks in the dream. Unusually long, thick, or lustrous hair, well beyond what's realistic, is read favorably — growing wealth, status, or luck accumulating visibly.