Yes! WetVet is quite right!
The greater the volume of air passing through the first stage the greater the likelihood of a freeflow. It's a simple application of the physical law that governs the adiabatic drop in temperature as a pressure drop in a gas occurs. That's how a refridgerator works and lots of other cooling devices.
A refridgerator compressor raises the pressure of the coolant gas just as an air compressor fills your tanks and heat is given off as it does so. Feel the back of the fridge. It's warm like your freshly filled tank. The greater the pressure of the gas or the greater the volume being compressed, the greater the amount of heat given off.
Then the opposite occurs. The coolant is allowed to drop in pressure as it flows through a reducer (read: regulator). As the pressure drops, heat is absorbed so the surrounding structure (the ice box) gets cold. The greater the pressure drop or the greater the volume of gas passing through the reducer, the greater the amount of the temperature drop.
In the case of your scuba regulator, any moisture in the reg will freeze or the moisture in the air may reach its dew point and condense and freeze. This can occur in water temperatures as high as 40 to 45 degrees F.
Two people breathing off a reg creates a condition more likely to result in a freeze-up and free flow.
Unfortunately there is no regulator system that will not freeze given the right circumstances. Some have special features that may reduce the likelihood but they all can be made to freeze up in normal cold water diving. Two hose regulators from years ago were very good in cold water. Regulators with environmental protection are usually a little better but not for the reason you may think. Store staff will tell you that they keep the water out so they don't freeze but it's not the surrounding water that freezes any way. It's the water or moisture inside the reg that freezes. Environmentally sealed regulators (Sherwood, Genesis and to a lesser extent those with an add-on rubber kit) will still freeze but are slower to reach the temperature that causes it. So slow that they may not freeze during a dive. Every regulator made will freeze. I've been on training Ice Dives on very cold days and even seen several Blizzards freeze up.
With a good sealed regulator, kept warm until the last minute, well-maintained, using very dry air, not breathing from the regulator until well underwater and not engaging in activities that require large volumes of air, you may dive in very cold water and have no problems.
All this is covered in any good equipment course or ice diving course.
One thing that's not been discussed is the increased likelihood of a freeze-up and free flow on deeper dives. The deeper you go the more volume of air passes through the regulator and the greater the adiabatic temperature drop.
Check out Doppler's thread under "Procedure for Dealing with a Free Flow" for more good ideas.