Hi Walt-
Saignelegier is really not all that far from Basel.. One hour and 40 minutes by train; twice per hour except at lunch time, where there is a one hour gap between trains. And, it is a major center of “horse country” for Switzerland. Annual major meeting days, etc. Of course, as noted, it is not the Alps. It is the Jura mountains.
Read down this page:
http://www.myswitzerland.com/ en-us/saignelegier-franches-montagnes-freiberge.html
If that first offer does not work for you, because of the overnight, follow the other leads from Snowman. There has got to be something available there.
However, you should keep in mind that in the Swiss Alps, depending on elevation, late May will likely have snow covered trails at high altitudes, and muddy ones at low altitudes. Altitude is critical. In general, the best Alpine scenery….say above 2000 meters… only really gets free for hiking (etc.) sometime in June.
Typically, this hiking trail at about 2200 to 2000 meters opens on about June 15th:
http://www.myswissalps.com/hi king/maennlichen-kleinescheidegg
I’ve not seen horses on it. Some parts are pretty narrow
Technically, you could still be in the Alps if you were be on the valley floor at Lauterbrunnen or Stechelberg, which is at about 800 meters and would almost surely be free of snow even in early May.
But, as you can see from the attached picture taken from Wengen, you wold not be up among the Alpine peaks. Unless there is unusually warm weather…and it has been warm…. the truly Alpine experience is unlikely to be available in late May and early June. And, a lot of places take there “between seasons” break in late April and May, reopening in early June. So, you should keep that in mind in your planning.
At the elevation of Basel (235 meters) or Luzern ( 435 meters) , late May/early June is definitely Spring.
Lauterbrunnen is at about 800 meters; Saignelegier is at about 980 meters.
Your relative in Basel can help you with information about higher elevations.
I’m curious – was the facility in Pontresina available on your dates?
Slowpoke