I'll say this, and then move on from the topic. I'm a local NY'er and a loyal Jets fan. I've seen countless games at Metlife and old Giants Stadium before that. Personally, there was only one time where the lack of a roof was an issue. That was last season when the Jets hosted the Raiders. It was a chilly and rainy Sunday. Other than that I've never had complaints about the venue being open air. As Pesto said above, Fall in the NY Metro area is great. Crisp cool air, and mostly sunshine. Sitting in the sun in a light jacket, or just a team jersey is a welcome experience. Beyond that there are tens of thousands of fans tailgating in the same weather hours before kickoff.Side issue: actually fall in NY is great; easily the best time of year and perfect for outdoor football. Of course, there is the odd hurricane but that would probably cancel an indoor game as well.
I agree that local customs, taste and income levels are the critical factors. Some places are happy with bitterly cold weather and no roof (Green Bay, Buffalo). Others make different decisions based on their best judgments of local demand.
On the topic of extreme weather, I went to the Rangers vs. Islanders Stadium Series at Yankee Stadium, and the Winter Classic at Citi Field. Both were in the middle of extreme freezing temperatures, I mean teens to almost negatives. I remember at Citi Field my lunch froze as I was trying to eat it. Nevertheless both times the stadiums were sold out packed with fans. Part of the experience was the weather. Again as a local I can say for most NY sports fans the weather extremes do not bother us. I've seen stadiums packed in heat waves and blizzards.