The boxwood shrub on the right seems to be showing signs of winter burn. This browning can show up when temperatures start to warm up after winter. Basically, winter burn can occur on all plants that have their foliage exposed in the winter, such as: some conifers (pines and spruces), boxwood, holly, and rhododendrons. I have been seeing signs winter burn on pine windbreaks.
Winter burn or dead foliage is not a result of cold temperature injury or disease. Basically, plants transpire or release water from foliage (photosynthesis) and a higher rate of water loss from foliage may result in high winds. If the ground is frozen or dry, these plants are unable to replace this water loss. The result is can be dehydration, foliar damage (winter burn), or even death.
What can you do about winter burn?
1.) When landscaping, choose plants that are less likely to be prone to winterburn
2.) Avoid planting conifers, boxwood, holly, and rhododendrons in areas that have high wind exposure
3.) You could put up a wind break to protect the plant
4.) You could wrap small plants in burlap or other material to protect from wind and water loss
5.) Products called "antitranspirants" can be applied to winter burn prone plants, but there is no research available, that I know of, that would prove their effectiveness.
Boxwoods can be pruned in the spring in order to remove any injury that has resulted in the winter.