One other factor that is in play with weather is the playing surface in question. Fields like the new Cardinals' stadium (which is on a gigantic tray that goes out-of-doors during the week, but then comes indoors under the retractable-roof dome on game-day) are obviously not much affected by prevailing weather.
Giants' Stadium used to be a mess late in the season when the field was tore up and the weather was foul (during the "grass trays" era, 1999-2001), but the Field Turf field (installed for 2002 and to my knowledge still the playing surface at the Meadowlands) has performed better during autumn/winter weather.
As other posters have pointed out in this thread, really severe weather (torrential downpours, high winds, arctic cold) are the factors that most impact production. Downpours waterlog the turf and make footing and ball handling more problematic (Dolphin Stadium in Miami often has games where precipitation becomes an issue, for example); high winds (Arrowhead Stadium in K.C. and Soldier Field in Chicago are notorious for this condition during the winter, to name 2) push the ball off-target; and Green Bay's Lambeau Field's (also Ralph Wilson Stadium in Buffalo, as another example) arctic temperatures in late November-early January make the ball hard and slick, and the field hard and unyielding.
During early autumn, weather conditions usually aren't as big a factor as they become later in the fall/winter, although in the Florida venues (Jacksonville, Miami, Tampa Bay) heat and humidity can be a test of conditioning/hydration for teams early in the season - Arizona used to be in that club until this year's opening of their new retractable-roofed stadium.
My .02.
