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She needs to be a bit older to do martial arts. They tend to need to know their left and rights. My daughter went at 5 and she found it difficult despite being tall and coordinated for her age. Will prob try her again when she is about 7. The council have horseriding lessons off western av but again they only take older children.
Have you thought of gymnastics? It's good for core muscles, stamina and strength and a good base for most types of dance. Capital academy gym in cardiff is excellent, they seem to be very knowledgeable and lovely with the little ones.
Taekwando lessons in Tremorfa Community Hall. Beginners on Tuesdays and Wednesdays 5.30. He takes youngsters from as young as 3 if they are interested/keen and is very good with the little ones. One of my ds's friends there started when he was three and is now an amazing 8 year old black belt!