26-16-3a. Limitations of public use of state controlled Wildlife Management Areas
(a) Target shooting is prohibited on any wildlife management area unless so designated by the Department.
(b) All-terrain vehicles, motorcycles, snowmobiles and all other motorized vehicles shall be prohibited on any wildlife management area unless so designated by the Department.
(c) Horses and other riding animals shall be prohibited on any wildlife management area posted against such activities.
(d) Except as provided section 26-16-2, camping is prohibited on any state controlled wildlife management area, except on the Sessions Woods Wildlife Management Area where camping, conducted in conjunction with an educational program approved by the commissioner, shall be permitted only if authorized in writing by the commissioner.
(e) Wildlife Management Areas shall be closed to the public from one-half hour after sunset until one-half hour before sunrise except for hunting, fishing or other activities authorized by the Department.

Higganum Meadows is not in my district so I don't know if it is posted against horses or not. If not, then legally they can be in there. If it is not posted I would suggest calling the Wildlife Division at 860-424-3011 to make your concerns known. They are responsible for determining what is and is not allowed in each WMA.