Notice, I said MOST, not all. In a freeze up (icing) conditions most will freeze in the open position.
I suppose we are talking at cross purposes, you are specifically referring to 2nd stage and I am considering the whole reg. Logic tells me that the 1st stage is more likely to freeze than the second stage, as the pressure drop is greater across it and therefore the cooling is greater, but then logic can be flawed!
I would contend that as far as 1st stages go.
1. all balanced pistons are downstream
2. all balanced diaphragms are upstream
It seems to me that for cold water, diaphragm regs are generally recommended. Then most cold water regs have upstream valves?
I would like to know if a failure (not freezing) is more or less likely to be free flow in a diaphragm vs piston reg? Don't seem to be able to reason this one out myself, other than diaphragms are more likely to fail closed, hope I'm wrong as I use diaphragm regs!