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Hi, I'm sorry to hear that you have been having problems with your horse. You are correct that the swelling could be arthritis especially if there has been little change in the size of the swelling over a long period of time. However I would still advise that you get your vet to check the swelling as other causes are possible. Your vet may need to take an xray of the leg in order to see if the swelling is related to bone, the joint space or the soft tissues, they can then advise you on the best course of action.
Hope this is useful, let me know if there is anything else I can help you with.