Not exactly sure about NH specifics, but those signs out here generally mean no unlicensed off road vehicles. Your KK should be fine as its usually viewed as a "car".
Some places post those kind of signs to preserve the car width two track with some grass down the middle for dual use as a bridle path for the horses to walk on. The logic being the narrow ATV/dirt bikes will tear that up.
74 CJ5, 258, T14a/D20, D30/D44@3.73
12 Cherokee 4x4,3.7L,4RLE/MP1522,D30M/8.25"@3.73,215/85R16 mich LTX A/T2
"Non Vi Sed, Arte"