Most of this was covered above but to sum it all up in one post. There has always been a lot of debate about htis. It can largely depend on location as frost severity is different everywhere, so what is happening at one course may not necessiarily be the same for another nearby. For example a links course has less potential over a parkland course for even getting frost as the sea breezes will help keep the dew (and therefore frost) at bay, simiarily a course may have open holes that get sun and other wooded holes that don't and the potential for damage can vary even on one course.
If it is only a very light frost then the damage is very minimal or even non existant as the dew on the leaf may be frozen but it isn't cold enough for the plant cells to have frozen. This is usually more likely a senario during the start and end of frost season but it depends on location.
If it is a heavier frost then the potential for damage is greater as the frozen cells burst when pressure is put on them which depending on severity can kill the plant. It then comes down to how much each club is willing to accept the damage. Usually the brown footprints, tire tracks or whatever look bad for a while but it will, over time, grow out. Of course the height of the turf plays a big part of this and greens height turf will take a lot longer to heal, so therefore will look bad for longer. Again a few footprints will not be detrimental but as the attached picture below shows, it is greatly compounded, even by one foursome.
The third item to look at is when you get a hard frost over a few days and the soil freezes. I have no problem letting golf out once everything is frozen solid as there is little potential for damage but (and it is very difficult to do this) I keep golf off when on the nicer days, where the day temperatures get high enough to thaw the surface (inch or so), there is huge potential for damage (This can be very frustrating especially when the night temperature get really low and refreeze everything at night). When the soil/roots etc are frozen an inch or so down, as you walk on the greens, the unfrozen roots near the surface can sheer at the frozen/unfrozen interface severly hurting or even killing the plant. The severity of the damage depends somewhat on how wet the surface is upon thawing ie the wetter the greater potential for damage.
I am a firm believer that anyway we can minize stress/damage in the winter, the less the plant has to recoperate in the spring and can use all it's energy to grow (and build roots) in preparation for the summer which is much more important, and again this depends on your location and how severe the summer stress is.