First off - have regulators suitable for cold water...
Secondly, you can breathe off a free-flowing regulator, and can make your ascent using it.
Additionally, this is where an auxiliary air source allows you to shut off the offending regulator and see if it thaws. This can be a pony. doubles or a buddy. I'm not a fan of the buddy option as it stresses the regulator, and can lead to the same thing. It does however beat doing a CESA - the last resort.
This is our SOP for here in the Great Lakes where most diving is cold water diving.
YMMV
+1
When I used to dive cold water, I always had some form of redundancy. Doubles or a pony. I also used regs that were designed to handle cold water. In an uncontrolled freeflow, switch air sources and shut down the free flowing regulatory. It's simple as long as you practice it frequently. CESA should be your last resort regardless of depth.
Also +1 on the downside of the buddy option as your alternate air source. This option doubles the load on the one regulator and can easily trigger another freeflow. There was a double fatality at Gilboa years ago where they believe this is what happened to two divers at depth. One had a freeflow, switched to the alternate air source provided by their buddy, that reg then freeflowed, and they both died. This was at least the leading theory. Given that both died, no one was left to say exactly what happened.