Thanks for the advice! I have noticed that many people who ride with a halter under, are using western curb-type bits.. with horses that neck-rein. So I guess in that case, you're not relying on mouth pressure anyway unless you're stopping, and then it is only light.. But yes, your seat and weight and other things are really your core means of control.
I ride my one mare in a bosal.. but she goes fine in a plain halter with leadropes!