We're hoping for a long weekend in the BO in late May. The walk to Klein Scheidegg is an important part of our plan. What is the likelihood that the trail will be open then?

For me the likelihood has been 50%. I visited once in late May and the trail was open. I also visited in mid-June and it was closed. I guess it depends on how much snow they had in the winter and spring.

As Edward says, there's no way of telling. Summer doesn't start until June 1st, but in the mountain that sort of date is meaningless - late snowfalls are possible at any time.

This website reports on snowfalls - it is meant for skiers, but Männlichen and the Kleine Scheidegg are on display, so you'll get some information out of it. It's only in German, but very easy to understand.

https://www.jungfrau.ch/de-ch/live/pistendaten/

And this website has phone numbers where people are bound to know the answer to your question when the time comes:

http://www.maennlichen.ch/en/grindel...leway-241.html

Hope this helps.

Don't worry: in the case there should be some snow along the "official" trail, you can just take the lower one via Gummi - Bustiglen to Kleine Scheidegg.
I suppose you know that there will be no gondola to Maennlichen until May 20th.

Based on these comments, I'm probably going a week later to be sure the cable car is open. Once up at Mannlichen, I will take the Panoramic Way, if open, or the lower trail. This revision should make it likely that I won't be disappointed.

"This revision should make it likely that I won't be disappointed"
May be. Never foget that weather is always unpredictable in the Alps. Nobody can exclude rainfall during all the time that you will be in the area.

Nobody can exclude rainfall during all the time that you will be in the area.>

and for days on end at times - any time of spring -summer - fall - keep schedule flexible - day trip out on rainy days - say to Bern or Lucerne. Value of having a pass is that you can do that without thinking about how much it costs.