If a city like Zermatt, Switzerland were to offer an electric car with a range of 500km free for the first year and with a small  charge after that, how long it will take for all IC car owners to give up their vehicles and switch?

In a city like Zermatt, Switzerland, I would be very careful with t...

If it's a government, only if it isn't my government. If it's a company, then no. Why? Because whoever is making that offer won't be around very long.

Impossible.    A car covered with solar cells all over will pick up maybe 100 watts, at high noon on a sunny day.  That's about 1/10th of a horsepower.  That's not enough power to push a car even 5 MPH against tire friction.  And that's the best case.  So, can't happen. if you let it charge up batteries, you can leverage that into a few horses for a few minutes.  Not enough for most purposes, and very far from making a car that people would ever buy.

If it were the government offering, I would not switch. If it were to be offered by a company with a good track record, I would switch yesterday (assuming it confirms to safety standards and it is reliable). Even if the range was 300km and not 300 miles.

If I lived above the Arctic Circle I would not touch it it because I would not be able to drive it for six months out of the year.