look for 'schlaf im stroh' - to 'sleep in the straw'.

There is one I can recommend in Eschenz. He caters for groups who ride around lake constance...

http://www.abenteuer-stroh.ch/

The weather in March will be 'spring' - cold nights, warmer days, the snow will be mostly gone, and several days of what I consider 'light' rain would be the norm.

I would recommend a combination of train and hiking. It's only an hour express-train to Schaffhausen from Zurich and from there you can see the Rhine falls, and go up-river to the medieval town, then stay at Eschenz and continue the next day along the river as far as you like to maybe Arbon, there is a caravan park there on the lakeside. Then from there it's possible to go to Liechtenstein and end up in 'Heidiland'...

Rather than being stuck close to Zurich I would recommend doing hikes along the valleys - one around lake constance, one down the valley in Ticino (Bellinzona), maybe from Bad Ragaz (Heidiland) and through Liechtenstein.

It really depends on how far you think you can cover in a day...and if you prefer to hike through the mountains and challenge yourself, or have more fun hiking along the flatter trails and enojoy the scenery...

Whatever you do, make sure you leave a good detailed itinerary, travel with at least three people in the group, and have good health insurance. They weather can turn pretty challenging and the terrain is fairly challenging if you get caught out in exposed land - and it's very easy to get disorientated in the forests and mountains...

What fun!