What to do? Wait. Patience is the one great gardening virtue.

Either it will come back when new growth comes in, or not. It isn't something that is under your control.

As for next winter, assuming the two are the same, does this one get more winter sun? Box doesn't like sun during the winter, and will often burn unless shaded.

I have same problem. My boxwood is facing south, and that is where winterburn occured. Although, it has been in this location for a long time this is the first time it was affected. So just wait and see. A little bit of compost would be good to spur growth.