Mars has no rainy season. In fact, it has no rain at all. There is a lot of
water on
Earth, and the range of
temperatures on the
surface and in the
atmosphere is such that water can change back & forth between solid, liquid & vapor. Indeed, this ability of water to experience a
phase transition is the primary driver of what we normally call "
weather" on Earth.
But on Mars, things are very different. The range of temperatures is far larger than is the case on Earth, but except for some few extremes, the temperature on the surface of Mars is almost always well below the freezing temperature for water, and is literally always below that temperature in the Martian atmosphere. And because the atmosphere of Mars is only about 1/1000 of the density of Earth's atmosphere, it could hold very little water vapor anyway, even if it were warm enough. Since there is no way to get water vapor to hang around in the atmosphere so it can condense into liquid, there is no way to get rain on Mars.
So far as I know there is nothing else that can rain on Mars either.