hi there,
wouldnt do it when it is actual freezing. As long as it is some degrees above freezing u should be fine. You can hardly kill privet by pruning it. If you reduce its size that much it is wise not just to whack it down but to cut out the oldest/thickest branches right down to the base and thin it out somewhat. Thus you get stronger new shoots.
Perhaps that helps, bye, Lin

you do not renovate an old shrub.. or privet.. by simply cutting it halfway down ....

what you will end up with.. next summer.. is green on the sides.. and a big brown hole on top ... which will take a few years to cover back up ...

read thru some of the articles at the link ...

and good luck

ken

Here is a link that might be useful: link