There is some ambiguity as to which was the first. An 1898 Canadian stamp had 'XMAS 1898' printed at its bottom, the rest of the stamp was a map of the world. For an image, see the link.
"In 1937 Austria issued two 'Christmas greeting stamps' featuring a rose and zodiac signs. In 1939 Brazil issued four semi-postal stamps with designs featuring the three kings and a star, an angel and child, the Southern Cross and a child, and a mother and child. In 1941 Hungary also issued a semi-postal whose additional fees were to pay for "soldiers' Christmas". The first stamps to depict the Nativity were the Hungary issue of 1943. These were all one-time issues, more like commemorative stamps than regular issues.
The next Christmas stamps did not appear until 1951 when Cuba issued designs with poinsettias and bells, followed by Haiti (1954), Luxembourg and Spain (1955), then Australia, Korea, and Liechtenstein (1957). In cases such as Australia, the issuance marked the first of what became an annual tradition. Many more nations took up the practice during the 1960s. In 1937 Austria issued two 'Christmas greeting stamps' featuring a rose and zodiac signs. In 1939 Brazil issued four semi-postal stamps with designs featuring the three kings and a star, an angel and child, the Southern Cross and a child, and a mother and child. In 1941 Hungary also issued a semi-postal whose additional fees were to pay for "soldiers' Christmas". The first stamps to depict the Nativity were the Hungary issue of 1943. These were all one-time issues, more like commemorative stamps than regular issues."
First Christmas stamp of Australia, 1957.
https://en.wikipedia.org/wiki/Christmas_stamp
