Is it a League decision, controlled by the Officiating Crew, or at the discretion of the Home team?

Actually... it's all on the team organization.

Most will keep it open 50+. Then close it anything lower.

My neighbor works for the Colts organization and we actually talked about the new stadium during dinner. He has a ring, it's awesome, but he showed me a pic of his ring next to Booger McFarland's... the Colts organization rings are nothing compared to the players and coaches rings.

Roof must be open if over 60 degrees.

I thought I heard last year somewhere that in regular season games the home team decides. In the playoffs, the NFL makes the decision.