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Exactly. The problem with this article is it tries so hard to pinpoint the exact date that it makes inexact assumptions such as:

Who get born exactly nine months after the conception date? As father of three daughters, I know the conception date for two of them due to circumstances of my wife being away and us making up for lost time, if you catch my drift. For the third (our first), we were doing the conception activity nearly daily or more, so it could've been exactly nine months, but unlikely considering the more was concentrated during a vacation period in late December and she was born in early September, so the more likely explanation was that she arrived a couple of weeks early. Possible, sure, but unlikely.
A major calendar change happened during the changeover from Julian (Roman) style to Gregorian (Catholic) style in various phases over a period of centuries, with England and the American colonies being the last hold-out in the 1730s. So any exact date is going to be moved out anyway. Some Orthodox sects celebrates it on January 6th, for instance.
The solstice theory is not without validity as burning yule logs and firing flaming arrows into the sky to relight the sun dates back to and even before the birth of Christ. With the crudeness of ancient time measuring devices, December 25th, or whatever it was called by the local calendars, would be about the first day ancients could tell that the length of daylight was finally growing longer again. It would have made a perfect conversion tool for early Christian missionaries and, by most rudimentary accounts, actually was.
The rainy season in Bethlehem runs from about late September until early May, so it is possible, or even probable, that shepherds could've been in their fields at anytime during this time period or perhaps longer. Recall also that the region had much higher rainfall at the time. In the Hannibal era (200 years earlier), savanna animals, including elephants, inhabited what is now the northern edges of the Sahara Desert, making it inevitable that areas further inland to the Mediterranean Sea would have received more natural rainfall than they do presently. This would have lasted until at least 200 a.d. when the Romans begin to encourage emigration to the British Isles from North Africa as desertification crept closer to the Mediterranean Sea. In short, while it doesn't disprove shepherds were likely in their fields in late December, it doesn't pinpoint it either.