Answer: Summer
Why:
The four towns that were named are the four symbols of the Chinese constellations — Suzuku (Vermillion Bird), Byakko (White Tiger), Genbu (Black Tortoise) and Seiryuu (Azure Dragon). Each of those divine beast represent a cardinal direction and a season. Suzuku is south and summer. Byakko is west and autumn. Genbu is north and winter. Lastly, Seiryuu is east and spring. The princess stayed in the south town, Vermillion Bird or Suzuku meaning her wedding was held during the summer.
Divine Beast Creatures
Suzuku = Vermillion Bird = South = Summer
Byakko = White Tiger = West = Autumn
Genbu = Black Tortoise = North = Winter
Seiryuu = Azure Dragon = East = Spring
