In my sci-fi story, I have a binary star system with two Sun-like stars orbiting each other in nearly circular orbits. The separation allows them to have planets in stable orbits, and their habitable zones slightly overlap, at least at the closest approach. (Or maybe the Primary, which has a few per cent more mass, can have planets in stable orbits while the Secondary can't.)
A planet orbits the Primary in a highly elliptical orbit that takes it from one edge of the habitable zone to another. And it has 45 degrees axial tilt. Water covers most of its surface, land mass is isles and archipelagoes, with the largest being slightly smaller than Australia. Adding some numbers: The closest approach to the star equals the smallest distance between Sun and Venus - 0,718 AU. The farthest distance from the star would be about 2 AU or a little more than the largest distance between Sun and Mars.
Thus, when the planet is on the closest approach to its star and its Southern hemisphere is pointed against the star, it has a short and severely hot summer, while the Northern hemisphere has a short and mild winter with average temperatures slightly below freezing and a lot of snow. In contrast, when the planet is farthest from the star (and travels in its orbit the slowest), the Northern hemisphere has a long and temperate Summer with bountiful agricultural harvests, while the southern hemisphere has a long and severely cold winter.
The question is: how long would each season be? What other circumstances should I consider?