Actually sandy no you won't.
I had my hysterectomy last year. Not all total hysterectomies include a double oophrectomy as well. With out the oophrectomy you will still have your ovaries. Many women keep their ovaries so they do not need hrt.
I am not menopausal and neither are many of the ladies who frequent the same hysterectomy support site as myself.
A total hysterectomy means they remove the cervix as well as the uterus. I retained my cervix so my hysterectomy was a sub total hysterectomy.
You can have an oophrectomy of one or both ovaries and not have a hysterectomy.