I can't see why not but if it were my hedge, I think I would cut it back in stages. Perhaps a foot at a time and see how the hedge reacts.

What type of conifer do you have? Some conifers don't take kindly to drastic pruning and will never recover. You'd be tempting fate. The general rule is don't cut more than 1/3. I'd go with Jimmy's suggestion.

If its a Leylandii you can cut it back whenever you like as long as there's plenty of green below the cut.Cut the trunk but leave the side branches that are growing up around it from lower down. They will meet eventually and carry on as normal Just don't cut it straight across the top.We have done this successfully during the growing season.

Best not risk this with with less vigorous ones though.