It follows the outbreak of equine flu in horses.
A message on the charity's website says while their donkeys are not affected, they're closed as a precaution.
Four more horses have tested positive for equine flu - this time in Newmarket.
Racing is on hold until at least Wednesday while the British Horseracing Authority tests horses nationwide.
Two race meetings have been cancelled at Exeter Racecourse over the past week.
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At the moment is it protected green space
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'Further falls are likely. Don't risk your safety'
