The major problem with your theory is that only 2 players are on the team from most of those seasons. And I advocate replacing both of them. Tony Romo's #s fade significantly in December. For the most part, no one can attribute much of that to bad weather.
Barry Switzer was the team's primary problem (along with the GM who hired him). Unlike Romo and the current crop of Cowboys, Aikman had proven himself many times over by the Switzer and Gailey years.
A 4-9 December record for Dave Campo is virtually the same winning % as Sept-Nov winning % for Dave Campo. His December record would only be relevant if they actually had any success before December.
The Cowboys were essentially a .500 team under Bill Parcells, 34-32, I believe. A .500 December record doesn't suggest anything, other than the Cowboys were the same in December as they were Sept-Nov. And if you want to joke about "the Great Bill Parcells", you should recall he's essentially the only person associated with this club since Emmitt Smith left that had any history of success at all.
On the other hand, the Cowboys are 22-4 from Sept - Nov under Romo, but only 5-10 thereafter. Most of those other seasons, the Cowboys were bad in December, because they were a bad or mediocre team, and their record showed it. But under Romo, you have a team that has won 85% of its games pre-December, but less than 35% after November.
The same fans who want to try to use #s to justify Romo in some historical context continue to ignore or omit those which matter most.