As far as I know, only one hair is allowed at a time.
[23:23:53] <AndChat|700625> Blue eyes ultimate dragon best card
[23:24:29] <AndChat|700625> You know the one with 3 heads
[23:24:39] <~Lightningkid> just like my dick
[11:35:40] <box> Hampa suck
[11:36:21] <hampa> not the first to tell me that today
Some hairs conflict with each other, and one will not be visible when both are activated. However, some hairs, such as the Santa Beard and Santa Hat, will both be visible if activated at the same time.
As far as I know, you can wear as much different hair styles that you want, I've seen mixes of candy locks w/ gentlemen essentials. Maybe it's changed tho.