Frost Beard (or Frost Hair) is a known phenomenon, but not well understood. We have seen it three times over the last five years, always in almost exactly the same location, a public footpath through Hen Wood on the Bathhurst Estate, running along by the side the River Frome.
The valley is subject to "frost pockets", cold air flowing down from the surrounding hill sides, and the air temperature can remain below zero in the morning when the Sun has warmed everywhere else. The general temperature was not below zero, and in fact the ground underneath the dead wood from which the "hair" is growing was not hard-frozen, and on the previous day (and later on this day) the ground would certainly be somewhat above zero.
The immediate cause of the "hair" is clearly super-cooled water emerging from very small pores in the dead wood, and immeadiately freezing on contact with the cold air. However, this does not explain why the water is forced out. Expansion of freezing water in the twigs may have something to do with it - but we seem to get so much "hair" from such small twigs that there may be a wicking effect pulling water from the ground. (The ground here is general fairly wet because of the nearby river.)
The last time we saw this (in 2014) I picked up a small length of twig with its "hair" (which of course quickly melted), took it home an put it under a low-power microscope. There was no sign of the pores through which the hair had emerged. They were clearly very small, or had closed up. I wondered if they were the result of a fungus infection, which might explain why we have only ever seen this in one particular location - though many nearby locations seems to have all the same dead-wood, frost-pocket and wet-ground characteristics.