In the most recent incident on 26 February the two girls galloped their horses over a green while a group of golfers were playing a morning game.
New Forest Golf Club in Lyndhurst said the greens were badly torn up and would cost about £1,500 to repair.
Both girls had dark hair in pony tails and were aged between 14 and 16.
"The girls ignored repeated requests from club members and made abusive gestures"
Police believe the same girls are responsible for other similar incidents on 16 and 17 February.
Pc Steve Ennew said: "Criminal damage caused to any property is treated very seriously by police.
"It is possible that these girls may not have realised the true extent of the damage they caused and the time and effort taken by golf club staff to repair parts of the course which were badly damaged."
Tony Taylor, golf club manager, said: "On the first occasion it was almost as though these girls were taking part in a gymkhana. We have never had problems with horseriders before."
Police said during the incident on 26 February "the girls ignored repeated requests from club members and made abusive gestures, before riding off towards the A35 and into open forest".
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©