I have heard that its a "no go" to use tent in Switzerland up on the glacier/near the huts. But is it true?

We are a bunch of climbers meeting in Zermatt for a 2 week adventure, where the plan is to go up on the glaicer and stay up for 3-4 days before heading down to valleybased campsites. Some of the participants are students and is on a limited budget (ie hut stay is out of the question)

Can we plan and execute a trip based on using tents ?

Please share your experiences

It's fine if you're in an out of the way spot, which I know can be kind of hard to find around Zermatt at this time of year. Around the less traveled parts of Switzerland I have seen people camped up nearby glaciers. At any rate, I don't think it's illegal to do, just frowned upon, so go for it.

Above Schönbielhütte, around point 3052 are sheltered sites where people obviously have camped before - from there you can climb Schönbielhorn, Pointe de Zinal or Dente Blanche. I would say the place is out of the way enough to stay there for a short period of time. I'm sure there are more places like this.

Though I'd bet free camping is forbidden in all the Swiss mountains...

The are some permanent places for tents above the Dom hütte on the normal route to Dom.

In 2009 there was a semi-permanent place for tents with built walls for wind protection right next to the path running from the Klein Matterhorn station to Castor/Pollux.

So yes, free camping is most likely forbidden, but you can do it.
However camping close to the huts and thus taking advantage of their "safety" whilst not paying anything, is by some people frowned upon.