Town forests may be established by action of the local legislative body pursuant to RSA 31:110 (so the first thing you need to do is to determine whether or not such an action has occurred — all it takes is for town meeting to call something the town forest). The town forest is to be managed by a town forest committee, which can be the conservation commission if the local legislative body so determines — if it has not, then there must be a separate committee. [RSA 31:112]
Revenue from the town forest goes to a special forest maintenance fund, which shall be non-lapsing (unless the local legislative body decides otherwise.) [RSA 31:113]
The statutes do not state that the forest committee (or conservation commission) have any direct control over the forest maintenance fund, so you should assume that any appropriations from it require the authorization of the local legislative body. Once such appropriations are made, however, then it is reasonable to conclude that the forest committee has the authority to expend such appropriated funds for the purpose for which they were appropriated.