Easy now.
My point is your organization is behind the times. Helmets are used, sans hats, in all levels of play. Pro, college and even the T-Ball World Series! You need to make a stand against this anti-helmetite organization, and free your head from the evils of wool caps!
Honestly, watch a few MLB games on the tube and see how many PU's have switched out to a helmet.
This same thing happened with inside chest protectors in the '60's. How many pillows do you see now? Bow ties, anyone?
See a beanie here:
http://www.honigs.com/detail.asp?Cat=2&Sub=37&Item=336
Depending on the helmet, you can wear a combo hat, with a little practice, under one. It works with my All Star helmet ok. It's doable, but very hot.