NIsan is an Assyrian month that corresponds roughly to March-April. Jesus was not born then.
The early Christians did not celebrate Christmas,. They thought Easter was important, for obvious reasons. After 300 years, they decided to have a holiday celebrating Jesus's birth. But they did not know when that was, according to surviving records. They picked the winter solstice to compete with the Roman holiday of Saturnalia.
But Christmas is decidedly NOT a pagan holiday.
The contention that Jesus was actually born in September comes from the "shepherds abiding in the fields with their flocks." Right after the harvest, shepherds were allowed to enter the fields so that their sheep would glean any spilled kernals and manure the fields. They were not allowed in before the grain was harvested and afterward there would be no point. So they would have "abided" there in late September, as that's when the grain was harvested.
