The word Hute/Hutung is derived from the same root as (cattle) herding - which is why we also speak of herding forest or herding pasture. Hude is a Low German form that can also be found in North German place and field names, not just the pure "Hude" (as in the case of Hude near Oldenburg - with the still existing Hudewald remnant) or Steinhude.
On the confusing forest pasture, the livestock (mostly cattle and pigs) had to be herded by a shepherd for the livestock owners of the village community, who was paid for this with the herding money. Children were also used (but mostly for goats and geese). This was also common in the past in the Alpine region and is still common today in many developing countries, where children herd the livestock of entire communities. The pasture (or forest) used was previously either communal property or belonged to the (feudal) landlord and, like the arable land, could be used as common land in return for taxes. The pasture (Hutung, Hute/Hude) was also a term for the right to graze or to fatten.
The pasture law developed a detailed set of rules. Normally, the owner of the pasture land was entitled to share the pasture. The pasture of various owners or members of a village community, for example, was called the pasture pasture. In certain circumstances, the land owner claimed the privilege of being the vanguard.