I am currently living in Germany as a Croatian national. In a few short months I will start my higher education in Switzerland and later MBA as well which total duration will be more then 4 years. I can also speak a little bit of Schwiizerdütsch. I know there are some problems with Croats seeking to live and apply for a job in Switzerland. So basically my question is: If I am a student in Switzerland can i apply for a one-year visa to work and live there and later extend it?
You may in any case apply for a permit, even to look for work or set up a business. The main issue is that, as a Croatian national, you are not (yet) covered by the EU freedom of movement agreement with Switzerland. That means more paperwork and time lost before being allowed to work than you would have experienced in Germany for example.
For workers, a prospective employer would have to show they could not find the employee they need locally (Swiss residents, no matter their citizenship), which could make it quite difficult for most people to qualify. The delay and increased paperwork make Croatian workers less attractive to employers (much easier for them to just hire a German or Romanian national for example). There is an annual quota for both long-term and short-term permits as well.
For students, the rules are less restrictive. I believe you might be asked to show you have “sufficient” financial means to cover your expenses in Switzerland. There is no annual quota. I would still recommend approaching the Swiss authorities as soon as possible (i.e. as soon as you have some registration confirmation from the university) to see how you can apply for a permit. If at all possible, applying early would prevent getting stuck waiting for a decision. Another effect of the current restrictions is that you are more limited than other EU citizens when it comes to working next to your studies.
Note that these restrictions are slated to end between 2024 (no restriction but still a “safeguard clause” that can be triggered if the number of Croatian nationals exceeds a threshold) and 2027 (full freedom of movement). Consequently, renewing your permit and eventually finding a job in Switzerland — if you want to do that — should be easier when your four-year programme ends.