There are several reasons.
Firstly, because Jesus came as the light of the world. He, therefore, came in time of the year when daylight hours were the shortest.
Secondly, because the Gospel of Saint Luke says that an angel appeared to the shepherds on Christmas while they were keeping watch at night.
Thirdly, because the Gospel of Saint Matthew says the the wise men were guided by a star, and generally, stars are only visible at night. So like the shepherds, they found Jesus at night under the star of Bethlehem.