It is possible to fit in that much more skiing or boarding. In April most lifts are open 1 hours longer each day than in January. The following table can give you a idea of how much skiable area to expect open for a spring visit. While the table can give you a good idea of how much snow to expect, it is impossible of course to predict the condition of the actual snow surface far in advance. Even in April snow-storms are quite common.
Snow often falls right down to the village, although there it does tend to melt in a few days.
Unless you are already familiar with Zermatt, you might find it useful to study the Zermatt piste map in conjunction with the following table. Effectively still like mid-winter in terms of snow coverage. Powder snow can last on the northerly slopes. Skiing to the village is still possible thanks to snowmaking. Powder snow normally softens within a day when it falls.