You can purchase a dedicated helmet cover for riding in the rain; it's what I use because I ride in the rain a lot. It cost me $20 and I just leave it on all winter. Seems cheap to me for the extra protection from rain and cold that it provides.

Under the helmet I wear either:

- A baseball cap (the bill keeps rain off my face) or a cycling cap. Especially good if rain is hard and it's not that cold

or

- The hood of my rain jacket (good if it's wet and cold, traps heat around the head)

or

- Just a skullcap (good if it's cold but not raining very hard)