There are around 89 or 90 days in winter. The exact number in a given year depends on whether it is leap year as well as the dates of the winter solstice and vernal equinox.
The seasons were designated to coincide with the natural position of the Earth in relation to the sun and moon, which determines the length of days and nights. Winter begins with the winter solstice, which is when the sun reaches the southernmost point in the sky for those in the Northern Hemisphere or vice versa. It is also the day with the least amount of daylight. From that point, as the sun begins climbing back up in the sky, the amount of daylight increases until the vernal equinox, in which day and night are almost exactly the same length. This is the beginning of spring.