Spiders usually leave a silk thread as they move so that if they fall, they are anchored and can climb back to where they were. Generally the mass ballooning events in open countryside are the result of species of money spiders (Linyphiidae), usually the ubiquitous pioneer species, climbing to suitable heights to lift off using silk threads which catch updrafts to lift off on the rare days that weather conditions seem to be favourable for their dispersal. There are plenty of spiders associated with woodlands, so your threads are probably either the silk trails left as spiders move being picked out by the sunlight or a possible mass movement towards a location in the open above dense branches and foliage where they can launch themselves for dispersal. This is certainly not usually reported from woodlands, but on one occasion I have seen an adult crab spider Xysticus ulmi launch itself across a wide woodland ride (at least 100m) by producing a silk thread which gained enough lift to take it into the air.
