Why does hurricane season end in the winter?

Because there are hurricanes through winter. Remember Tropical Storm Zeta a few years back? That one was part of the 2005 hurricane season but actually lasted until January 2006. They've actually had to extend the official hurricane season to account for all the storms.

As for why storms start in midsummer but last through winter, it takes a while for the oceans to heat up enough to produce them, and then takes a while for them to cool off enough not to produce them.

A hurricane needs a sea surface temperature in excess of 26°C to form. These warm seas are less likely in winter than in summer. They also need an area of low pressure. This is usually the monsoon trough. In the northern hemisphere winter, the monsoon trough is south of the equator and tropical revolving storms there are affecting countries like Australia.