Have the horse accessed by an equine vet for lameness, then go from there. It does sound like arthritis, stiff & sore at the start of a ride but gets better as the horse starts moving around, means whatever synovial fluid is left is lubricating the joints with movement. There is many treatments for sore hocks, an equine vet can access your horse and explain the options to you. Until then, we are just guessing, it could be something very easily treated.
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Thank you! I think I will wait a few more days to look for improvement and have my vet come out!