When I went with a group I was told that they had requested permission from the MOD but the local council (think it is Carmarthen) should be able to advise you. Pembrey is another option. I have the tel no of the local stables where you can pay to park & have a map of the forestry route to beach.
ooh i've redden there... but with a local treking center... lovely beach for a gallop... most beaches have signs on them stating what you can and can't do at different times of the year... but yup - council should be able to tell you too.