I am heading to the B.O. in late May so I have been keeping track of the webcams throughout the region. The Gimmelwald webcam is a handy indicator since it is at the same elevation as Murren and Wengen.
There hasn't been much snow there this winter. The snowpack on the mountains around the town looks below normal for late March. Frankly, it's what I would expect from June, not March! Springs snows are always a possibility, but right now it looks like the folks planning April or early May visits to the region may have more hiking options than expected.
The Swiss Panorama webcam shows the higher elevations such as Maennlichen still have plenty of snow.
ETA: Does anyone know of webcams for Wengen and Murren which are not polluted with advertisements and "download now" nonsense?