Not all SP regs are prone to freeflow in cold water and saying they SP regs are prone to freeze ups" is an over generalization. The same thing is true when saying all diaphragm regs are less likely to freeze up than piston regs. Not all diaphragm regs are sealed and those that are not can often be very prone to frezeing.
The Scubapro Mk 2 Plus and Mk 16 are actually very freeze resistant and work well for ice diving. Their flow rates are low enough that their TIS systems are more than adequate to handle the adibatic cooling load.
The Mk 25 on the other hand has a reputation for freezing up in very cold water (40 degrees F or less). The S600 second stage seems to be associated with Mk 25 freeze ups more than any other second stage as the S600 has a tendency to develop a slight freeflow in cold water (as does my X650 so far).
Good cold water technique also goes a long way toward preventing a freeze up:
1) don't test (and consequently cool) the reg until the first stage is under water.
2) Don't breathe and inflate BC or drysuit at the same time or in immediate sequence.
3) use several small blasts on the inflator rather than one long one.
Using low presure tanks also helps as with a smaller drop in pressure, 2250 to 2400 psi dropping to 145 psi as opposed to 3000 or 3300 psi dropping to 145 psi, less heat has to be drawn from the reg and surrounding water as the air expands so the chance of ice formation is reduced.
Using good technique, low pressure tanks and D400 second stages I have never frozen up either Mk 20 or Mk 25 first stages in well over 300 dives in water with bottom temps ranging from 35 to 45 degrees. So the Mk 25 can freeze up, but if you do your part, it won't.
In general, due to the reduced effects of adibatic cooling as tank pressure drops, the largest risk of a first stage freeze up is early in the dive with a full tank. Second stage freeze ups on the other hand tend to result from a slow build up of ice in the second stage and they consequently are more likely to occur later in the dive.
Older metal cased second stages and plastic cased second stages with metal air barrels are less likely to freeze as they have much better heat transfer traits. With plastic case/plastic air barrel second stages, getting ice chunks spit at you is better than having the ice stay in the reg and collect until it jams the lever or poppet, but it is still a bad sign. But don't forget that if this starts to occur, you can always give it a break to let it "warm up" for a few minutes by switching to your octo or redundant second stage.
A first stage will always freeze open so that air freeflows, usually in huge amounts. A second stage on the other hand can freeze closed and fail to deliver air. The good news is that again switching to the octo is all that is required until the primary second stage thaws.
If the first or second stage freezes up with a resulting freeflow, turning off the valve to the reg for several seconds will normally allow it to thaw. Obviously a pony or other redundant air source is the way to go to enable you to wait for the primary reg to thaw.