Hello. I'm glad you've turned to AaEx.
This is winter damage but not the usual kind where the leaves of the shrub lost too much moisture from transpiration but due to the severe cold we experienced last December and January before the snows came to blanket the shrubs. This appears to be minimal damage where those branches and twigs have been killed outright. It's not likely that any other part of the shrub has been affected.
If it were earlier in the year (before the end of July), I would have recommended pruning out the brown sections; but now if you prune, it may stimulate the shrub into new growth that won't have enough time to harden off before winter. So I recommend pruning out the dead areas next spring when the shrub has a better chance of starting to recover and fill in those areas. You'll need to prune back to live tissue to make that happen and it'll probably take a few years before those areas fill in.
Here is a full article on the issue from the U of MN Extension: https://blog-yard-garden-news.extension.umn.edu/2019/05/why-are-leaves-on-my-boxwood-brown.html