Like R Scott said it's all about keeping the water moving. All of Sepp's watering systems are spring fed, providing a constant source of flowing water. All of the troughs are nearly constantly overflowing with water moving through the system. I'm not positive but I imagine that all of the water lines he uses from spring to trough are buried below frost line. The water trough systems are all fed by a hollowed out log which is 24"+ at the base and the spout is a branch. I believe the r-value of most softwoods is around 1.4 per inch, so the water is actually insulated quite a bit while moving through the log. The water is also insulated by the snow and ground all the way from spring to spout. The water in the trough is always moving so a section of it doesn't freeze. Sometimes there was also a plant growing around the spout enhancing the protection even more.
At
Sage Mountain Center they also hit bedrock above frost line for running some of their water lines. They have had good success with insulating that section of waterline and building up the soil on top. If you have standing water in the pipes for long periods of time this makes the lines much more susceptible to frost. If you have a long section to go above bedrock there is also insulated waterline, I've seen them for wood furnaces.
For the pigs water it seemed to just run overground into a trough and beyond so that they can also wallow in it.