When this winter? The further from mid-December one gets the more comfortable and less challenging the 14-day push would be. That said, I can say, even with daylight hours this May (we had epic winds that tend to be non-existent in the winter) we found it a challenge to make enough miles to make it out in the allotted 16 days.
We launched Jan 9th I believe and took the full 25 days. But that included 5 layover days (maybe 6, time is eroding the memories already). We could have comfortably lopped off a few more days if need be. Much more than that would have been difficult that time of year from my experience. We oscillated from frigid to relatively warm. We only had one boat incident but that ate up half a day (wooden dory). The skill of your crew is something to consider as a team that is more experience and/or is efficient in the event of a flip will make a huge time and safety difference.
Coldness....December is worst from friends comments. Freezing temperatures are common and preventing the various forms of frost bite and moisture-related damage are imperative. Rain can be heavy and persistent thereafter. We had 6 straight days after a week of clear skies. Wet and cold weather can be mitigated but it its demanding physically and emotionally when it lasts that long.
Feasibility....depends on above factors and how much your crew is willing to adapt to the limits. Is your crew willing to get up before dark and rig no matter what? That becomes more important earlier in the year and could be make-or-break in the decision. What are the tendencies of the group? We are camp folks as much as rafters and love exploring the many side canyons (so much to see down there, and some of it is only feasible in the winter).
Would I do it in 14 days? Gut says no way but I know how rare and amazing the experience is down there so that is subjective and I wouldn't likely be so certain if it was the only way to see the Colorado. Is it possible? Almost always a way to make it happen if ya'll are willing to do the needed logistical efforts and be disciplined.
I wouldn't trade my winter trip for anything but it comes with its own challenges. I found it "safer" and more enjoyable than the May trip this year. If/when you decide there are plenty of previous threads here and others who have spent winter in the canyon. Some simple advice will prevent alot of issues. Just let us know what you decide and folks will step up to the plate with more explicit info.