Not sure if having a controller changes things, but on PC with KB/M, on the head inventory slot, there's a little checkmark in the lower right-hand corner. Check it to show the helmet, uncheck it to hide it.
Does this help?
I have been wondering the same thing. I mean why pick out a hairstyle and face if your just going to cover it up

I just tried to figure it out with my controller and it didn't work, but when I switched to keyboard, then hid the helm, then switched back to controller it was hidden.
If anyone knows how to do it on controller that would be awesome, if not hopefully they will add the option to in the future.