Murray has averaged 5.4 yards per carry in three career games against the Giants. He rushed for 86 yards on 20 carries in the Week 1 victory. Murray's five games with over 100 rushing yards include a 131-yard effort against the Giants in the 2012 season opener.
Aside from Murray's success against the Giants, some NFL teams tend to run the ball more when the temperatures drop and conditions worsen. On Oct. 20 against the Philadelphia Eagles, quarterback Tony Romo noted how difficult it was to throw in the windy conditions.
Sunday's forecast in East Rutherford, N.J. has temperatures in the 30s with winds coming in at 24 miles per hour.
"I don't think it's really that big of a factor," Murray said. "While you're out there, you're never thinking, 'Oh, it's hot.' You're never thinking, 'Oh, it's cold,' until you're on the sideline, really. It's not a big deal."
With the Cowboys' passing attack struggling, the run game could be a focal point against the Giants.
When given the opportunity, Murray has responded with solid games. This season, Murray has four games in which he's rushed for 70 yards or more. He missed two road games, at Philadelphia and Detroit, because of a sprained knee. In his absence, rookie Joseph Randle rushed for 91 yards on 33 carries with no touchdowns.
But in the Cowboys' last game before the bye at New Orleans, Murray was the only man to carry the ball and did so 16 times, gaining 89 yards with one touchdown.
Murray is never one to ask for the ball, even when the situation calls for it. He didn't have a single carry in the fourth quarter of a close loss at Kansas City in Week 2, and the Cowboys carried the ball a franchise-low nine times in a victory over Minnesota on Nov. 3.
The Cowboys are 11-0 when Murray carries the ball 18 times or more.
There have been other games in which a deficit of more than one score dictated more pass plays. Overall, the Cowboys have preached for a balanced offensive attack, but sometimes that hasn't occurred.
NFL teams are 34-20 this season when a running back or quarterback rushes for more than 100 yards. The Cowboys are one of those teams that have picked up a victory, when Murray rushed for a season-high 175 yards Sept. 22 against St. Louis.
"If we run it well, that's obviously going to open up the passing game and vice versa," Murray said.