Why is winter considered the end of the year when two of the months are in the beginning of the calandar year?

You've answered your own question - winter begins on the last month of the calendar year.

The placement of New Years Day dates back to the roman times. Older calendar systems placed the beginning of a year closer to the first day of spring. In other words, the date we start a new year is what ever the most people agree on and in the Gregorian Calandar, it is January 1.

A bigger question might be the placement of first day of any season since the seasons tend to run about 30 days behind the calendar. Why put the first day of winter in the northern hemisphere on December 21/22 when the three most winterlike months on average are January, February and March?

It's starts in December. The last month of the year. But I guess it's both because it's still winter on January 1 so it's both.