Contact the Council which the beach falls in and they will let you know what local bye-laws there may or may not be. Here in North Yorkshire I think you can go on from Oct-March/April.
You'll be able to find your local councils phone number in the yellow pages or local directory. I know most beaches over here allow horses, but some state from which time during the day they are allowed on (normally least busy time, early morning, late evening)
Our council classes horses as dogs! if there is a dog ban on the beach, (usually between Easter Day and 31 October)horses are also banned. Your local police station should have a map of the coastline, with all the beaches marked as either banned or allowed for animals