Bethlehem is a small town in what was the Judea region of Israel. It was the place where Jesus was born.
In this nineteenth century drawing you can see that it was a small town among the high hills of the region. Such small towns get very cold in winter and snow falls, even though in summer they are scorching hot.
That is the reason Mary and Joseph would have looked for a place of shelter in winter, for it would have been too cold to stay outside, and certainly too cold for baby Jesus.