Ok. I checked a few sites from... say, South Africa.
I would love to grow some of their small plants, succulents, or bulbs.
BUT
Most often it's mentioned "winter growing".
Does this refer to my winter (in the N hemisphere) or their winter (in the South)?
I don't think I want to have plants that all summer when it's nice, sunny, long day they just SLEEP and wake up now, when it's cold, freezing, getting dark before 5 pm and so on.

Not sure about this, but one South African plant I was researching recently indicated that it bloomed in the summer, and the site called "summer" from November to March. I would assume that "winter" is the cold season, no matter what part of the world you're in. But that is just an assumption. Is there a specific plant you're looking at?

Just a thought but here in the tropics, and South Africa has some arid tropics, there are many things that we can only grow in the winter because it is too hot or too humid in the summer. Like tomatoes, they will not thrive in the summer but do fine in the winter. So perhaps, they are talking about 'winter growing' as a time when temps are not as extreme?

Good point, Jonna! "Cold" is relative!

When people in the southern hemisphere say "winter growing", it means the plant is active in their winter (when it is summer for us). So most winter growing species, (from either hemisphere) that are hardy enough to survive our winters, will not perform well in climates like ours where it gets too cold for growth in the winter. When I look for South African Gladiolus species, for instance, I pay particular attention to whether the species is summer or winter growing, and generally stay away from anything that is a winter growing species. Some plants, however, might be tricked into thinking our summers are actually "winters" and you might be able to get them to grow in our summers. Obviously, they would need to be able to tolerate the summer heat you have, which is likely significantly warmer than any of their native winters (in South Africa, for instance). One could conceivably trick them by keeping the plant bulb dry and warm in our winter, and then giving it water in spring.

All that said, Jonna makes a good point that one needs to take into account the natural habitat of the particular plant(s) as an aid for your decisions. Indeed, I am trying a winter growing species of glad (Gladiolus cunonis) from seed. It was just too cool to pass up!

Have you visited the PlantZAfrica pages Calin? Lots of native plants and good information on culture there. In general Winter (cold June to August) in South Africa is the dry season and Summer is the wet season. Except for Zantedeschia aethiopica, which is native to marshlands, Calla Lilies thrive in our hot summers, if well watered. However, even in Florida winters they have a low survival rate because it's wet.