It's common for winter injury to remain dormant on evergreens, such as holly, until the weather begins to warm up. While the temperatures are still cold, the plant is not active. But with the arrival of warmer conditions in spring, the damaged water-conducting tissues can't supply the moisture needs of the leaves, and they turn brown.
It's worth waiting to see how extensive the damage may be before you take any curative measures. Some of the leaves may be damaged, but buds may not be, so the plant may send out new, normal shoots this spring yet. If, after the plant sends out its spring flush of growth, there still are browned areas, go ahead and cut them out early this summer.
Next year, make certain that the soil around the hollies is thoroughly watered going into winter. If the problem is severe, you may need to provide some shade from winter sun so that the leaves do not dry out too much over winter.