They do get a bit skinny in winter, its natural and you probably had lichen on it before - it shouldn't harm it. You will notice it leaf up in the Spring. My house is surrounded by privet hedge and its just the same each autumn/winter.

It may regrow next year or it might have a more serious problem.

I've noticed lots of examples of individual privet bushes within hedges die over the last year or two. I don't know what the cause is .

If the whole of your hedhe looks the same it will probably regrow. if it is just one or two individual bushes then these may die. All you can do is wait and see.

You might want to scrape a bit of the bark off of the "bald" twigs. If the inner layer just under the bark is moist and green, then they are alive, and will likely regrow. If the inner layer is dry and brown, abandon hope for those particular twigs, though it may still regrow from lower down. You might want to consider what kept the bushes from regrowing after cutting: drought? it was later in the season than you remember, i.e., early fall, rather than mid summer, etc.

Yes, I would suggest re-growth shortfall due to drought, but as everyone says above, privet is pretty well bomb-proof and should recover. If in doubt, a night with slow hose pipe watering once in a while will fix it, especially if you are in an area that has seen little rain this year. Also, if your hedge is between tarmac/concrete paths/drives etc it would not have got enough of whatever rain we did get this year. If you are in a hose-pipe ban area this winter - bath and sink water will still do the job, and not harm the hedge.

If you use the gray water, as suggested by Avkq47, above, you will still need to use the hose a couple times a year to prevent soap (and other cleanser) buildup in the soil, unless you get a really good, long, soaking rain. Organic soaps and cleansers help with this, but aren't a complete solution.