When can my baby start going out without a hat?

When it's...: ...Neither cold nor windy nor raining nor sunny. Don't forget about the hat as a sunburn and sunstroke shield. As for the child's age -- even adults should wear hats if they are prone to sunburn.

Personal choise: Babies have a relatively large head to body ratio and can lose a large amount of body heat to their surroundings. Body heat requires energy & to grow babies need to put the energy they have into growth rather than trying to stay warm. Hats help cut the energy losses & certainly should be warn when they are in cold surroundings at any age. Indoors, it is less of an issue.