The real difference is huge, especially on mountain roads like you're saying. Winter tires have a different rubber compound that stays more flexible in the cold, while summer ones harden up and lose grip. On top of that, the tread pattern is deeper and has more sipes (those little lines) to drain water and snow better. When the temperature drops below 7°C, winter tires start to make an enormous difference in braking and traction.
It's not marketing, it's tire science. If you're driving in mountains in winter, you can easily hit snow or ice, and that's where the difference between having winter or summer tires can be the difference between getting through and getting stuck (or worse). A C3 is a light car, so it also suffers more with unsuitable tires in tough conditions. Portuguese law requires you to have winter tires or chains on certain mountain roads during winter, so if you're traveling to those areas it's actually mandatory.
Investing in two sets of tires isn't cheap, but they'll last you years if you take care of them properly. The wear is slower because each set only works in its season. If it happens that you only do urban trips at sea level, maybe you could wait and see how winter goes, but with mountains involved I wouldn't risk it.