Cold water is better for your complexion.
From Jasmin Malik Chua:
Hot water whisks away the water-retentive fatty substances in your skin, leaving it dry-or in serious cases, cracked, which can invite infection and inflammation.
People make all sorts of claims about the benefits of cold water on the noggin. They say it makes hair shinier and prevents baldness. I can't really find any science to back that up.
In theory, however, hot water opens pores, and cold water shrinks them or at least makes them less likely to expand.
Do what you want with that information.