The account of Bielski Partisans is probably the most popular one, as it was made into a movie titled "Definace" staring Daniel Craig. They were a group of Jewish partisans that hid in the woods of Belarus from 1941 to 1944. Although they called themselves Partisans many of them weren't actually partisans at all. Most were Women, children and the elderly that had escaped from the ghettos and other occupied areas. Some heard about the safe-haven from partisan recruiters, and decided to risk their lives to find some relative safety. In all the group maxed out at about 1,200 people, only some 200 of those were actually Partisans.
The group did organically start out as a group of partisans, whom were lead by Tuvia Bielski and experienced soldier who served in the Polish army. His three brothers served as his lieutenants, and helped organize run and recruit in the organization. The group used the Naliboki forest as their hide out, and as they grew, more and more civilians trying to escape the Nazis ended up coming to their camp - which continued to grow overtime. The camp was situated deep in the woods, and its inhabitants lived in dugouts made with wood from the surrounding forest. The camp at its largest had all the amenities of a small village including a school, hospital, shops, and jail and even a synagogue.
As more an more refugees came, more skilled labor was found, and everyone was put to work in their pre-war professions for example, cobblers set up places to repair shoes, cooks worked in the kitchen, tailors repaired and made cloths, and so on.
While the civilians of the group stayed behind and worked in the make shift village the Partisans were active in the area, often hunting down German's and their collaborators, however, their main goal was to save other Jews and to provide food and materials for those back at the village. However, their partisan activities as well as other partisan activities in the area attracted too much attention. In 1943 they and other groups were hunted down by the Germans during Operation Hermann. Many were captured or killed during the operation, however The Bielski group manged to avoid some of the onslaught by splitting up into smaller groups and relocating to another forrest hide out in the area. At this point in time is was known for refugees, Jews, and gypsies to be roaming and hiding out in the woods. There we also other partisan groups affiliated with the Soviet's operating in the area.
So to answer your question, yes there are several accounts of groups hiding in the Forrest for safety during the war. However, this is the most popular one involving Jews whom not only hid but resisted the Germans in the occupied areas.
Edit: word