As a former leader that I worked with always said using the military term, you want “Fewer soldiers, better fed”.  A headcount freeze is an opportunity to increase hiring not freeze it.  The problem is that too many organizations mix up the intent versus the impact.  It is important to be very clear on the goal.  If the goal is to freeze employee expenses (salaries and benefits) at their current level, then a headcount freeze can achieve the same result as a hiring freeze, but in a much more effective manner.