If the weather is fine, you can wear ski goggles with a hat only.Most ski goggles are adjustable so as to fit the hat only. However, I think wearing ski goggles with a helmet is much safer than with a hat because the helmet can protect you when you are skiing in a dangerous environment.In my opinion, you can wear ski goggles without a helmet, but you'd better wear them.
Of course you can.Some people will wear ski goggles not with a helmet but with a fashionable hat. But I should say a helmet is much safer than a hat. If you just go skiing, you'd better wear ski goggles with a helmet.