No, not the whole airport! Just the famous Founders' Plaza viewing area.
Don't worry, though. It is moving to a new location!
The airport is closing the plaza and road leading to it, in order to make a new taxiway, and funding from that project is going to pay to move the parking lot, benches, and monuments all to a new location on the northwest corner of the DFW field, at the corner of Texas 114 and Texan Trail (or W. Airfield Drive?). Here is a google map of where I think the new location will be:
This new area will be perfect for late day shots all year because you will face east, and it appears not too far from the traffic line for 18R/36L. Not sure if you will get a good view of the taxiway though. but you can be sure that this will be a no-hassle photo-friendly place.
Founders' Plaza will officially close January 4, 2007. So get your shots now before it is forever gone. The new plaza is supposed to open within 90 days from then.