Members of the public are asked to keep dogs under control while tree works take place at Millennium Oakwood.
The Department of Environment, Food and Agriculture says it's had close calls with dogs off leads while operating machinery.
It adds that it's imperative that members of the public stick to path closures and keep their animals safe.
If dogs are not kept under effective control then the department will have to close the whole site for safety reasons until work is completed.
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