Don't tell me you actually thought that the shepherds had their flocks out in the mountains around Bethlehem in late December?
I don't take a position on the issue of when Christ was born. I do, however, strongly doubt if John's usage of skenoo, even if it was intended to allude to the Tabernacle, meant anything beyond the fact that Christ made his dwelling amongst men. This isn't a nativity narrative, so I strongly doubt if it is intended to suggest Christ's birthdate.