It is my understanding that there are no general rules of what constitutes a "low enough" dose for a "short enough" time to stop prednisone cold turkey.
It is best to err on the side of caution when in doubt. It's worth a call to the vet who prescribed it and ask what to do especially if there weren't clear directions printed on the bottle.
What to do next also depends on what condition is being treated. If you are thinking of stopping the medication due to side effects, your vet may feel it's important to keep your dog on this drug because the benefits outweigh the side effects.
However, for some severe types of side effects, the vet may feel it's important to stop cold turkey to prevent further damage (e.g., dog vomiting copious amounts of blood from stomach ulcers).