It all depends on the winter and spring weather. I don't live in Europe anymore, so I haven't been following the weather this year, and I don't know what kind of winter they've experienced so far
. Let me give some examples. Last year, the winter was unusually warm. The ski season barely made it into March in some mountain areas, and the trails were mostly clear by mid May. Two years ago, the winter was about average, but it was an abnormally cold spring. I wore a winter coat as late as early June. It was almost late July before many of the high altitude trails were completely clear of snow in Austria (I'm not sure about the Swiss Alps, because I didn't visit them that year). So in a nutshell... if you're determined to visit early, you just have to roll the dice and hope for the best.
Or an alternative- get you Alpine kicks in Bavaria or Tyrol. Some of the well-known resorts here have larger year-round populations, so they never go into hibernation quite like the Berner Oberland. Also, the mountains are not as high (but still impressive), so the snow pack usually retreats earlier. The Berner Oberland is kind of an outlier for what you have planned anyway.