There are three different Seasons in Lara Croft and the Temple of Osiris that can be selected by turning the mechanism inside the Osiris Shrine Interior part of the Overworld Hub Level. There is a second mechanism here that controls the time of day; the player can select whether it is nighttime or daytime.
The three seasons are summer, rainy, and winter. This is consistent with the actual seasons the ancient Egyptians based their calendar on.
In summer the land is dry and desert-like. Not all locations of the Overworld can be reached in summer at first. This is also the season when Lara and her companions enter the Overworld for the first time.
To change to summer one needs to turn the lever of the outer mechanism in the Osiris Shrine Interior to the south (bottom of the screen).
To change to rainy one needs to turn the lever of the outer mechanism in the Osiris Shrine Interior to the northwest (top left of the screen).
In winter the rivers turn to ice and there are several places that Lara can reach now that were inaccessible before, e.g. the Cliffside location of the Overworld.
To change to winter one needs to turn the lever of the outer mechanism in the Osiris Shrine Interior to the northeast (top right of the screen).