Q: " should I try persist with the pony classes or try again next year?"
A: Her fear can be dealt with by gradually exposing her to what she is afraid of. At first it may be observing others ride, then petting the pony, feeding it an apple, getting on the pony but not riding it and eventually riding it. These of course will not be all done in the same day and one of the behaviors can be used during one day and then progress to the next.
You may also speak to her about the fact that such things happen and that as she learns more about riding she would notice her level of confidence change. Let her know that the pony is not intending to harm her. Ask her to think of a time when something happen that also was not volitional ex: she dropped a plate, she tripped and fell down, etc. and how these actions in themselves do not lead to never carrying a plate or walking ,etc (help her come up with her own examples that relate to her or use your own that she's witnessed)
Avoidance is a defense mechanism and her fear is based on her experience and how she's perceived it. As she develops healthier coping skills (over time) she would be able to discriminate b/w things that are causing her distress such as the swimming or riding lessons and manage her internal dialog and subsequent feeling of fright.
Thank you for the prompt reply, I just wonder should I be concerned about how she deals with difficulties in her life, or is this something she develops with age and experience? The reason we started pony club was because her confidence was down after we had to remove her from swimming class due to her ever increasing phobia/fear of the water, and now that she has had this accident in the pony club I fear that she will again become so afraid that she will eventually have to give this up too! I worry that everytime she has difficulties in the future she will just not try anymore. Thanks again Grace