Plastic cased second stages with plastic air barrels are more prone to ice formation inside the second stage. if the ice formation prevents the poppet from closing, a freeflow results.
That type of failure was virtually unknown with the older metal cased second stages and was very uncommon with second stage with metal air barrels connected directly to metal inlet fittings and metal adjustment knobs located outside the case. That makes sense as the more metal to water contact, the greater the heat transfer from the comparatively warmer (above freezing) water to the colder internal parts of the second stage and in particular the air barrel or aspirator.
That said, traditionally the cause of most extreme cold water freeflows has always been ice formation inside the ambient chamber in the first stage that blocked movement of the piston or diaphragm and prevented the first stage from allowing the seat to closing the orifice. Thar results in excess pressue that is then vented by the second stage. The second stage may also freeze due to the sudden increase in cold air flow and adibatic cooling, but the first stage usually started it.
Unless you have a fully sealed first stage, I suspect the first stage is still causing most of the cold water "freeze flow" issues. However the fully sealed Mk 17 / S555 freeze flow experience makes the point that a great cold water first stage is still no better than the weakest link in the chain. The S555 is both compact and plastic so its surface area is small and being mostly plastic, the air barrel is not able to draw much heat as it is well insulated from the warmer water outside the reg. A really bad combination.
The Mk 25 has its own cold water problems as the TIS system is not quite up to the hgeat transfer/freeze prevention task in extremely cold water (below about 45 degrees) unless your cold water technique is perfect. When you combine it with an S600, with its small plastic case and plastic air barrel, you can have bigger problems. A very slight freeflow in the second stage caused by formation of small ice crystals can create just enough extra flow to cause the Mk 25 to begin forming ice in areas that ultimately result in a large freeflow.
My advice is to use a Mk 17 (an excellent cold water second stage that has been tested at high flow rates at 165 feet for 200 minutes with no freeze up resulting - a test the Mk 25 would not come close to passing) with a new G250V second stage as it has a metal airbarrel and large finned metal adjustment knob and inlet fitting nuts that transfer heat very efficiently. The original 80's and 90's era G250 is nearly as good and the older metal cased Adjustables and Balanced Adjustable are superb.
I also agree a long hose helps as it allows the air flowing to the second stage more opportunity to warm up.
In seriously cold water with any reg:
1. pull back the hose protectors to expose the metal fittings on the hoses to expose as much metal as possible to improve heat transfer.
2. Do not test the reg prior to entering the water. Iit supercools the reg as heat transfer in air is very poor compared to water
3. do not over breathe the reg and do not simultaneously inflate and inhale or wait to get to the bottom and then use a long blast of air on the power inflator to inflate the BC and or dry suit. Heat transfer requires time so pread the air usage over as much time as you can.
4 if practical, use low pressure tanks. the lower service pressure reduces adibatic cooling loads on the first stage.