Definitely bundle up. Scarves, gloves, etc. Make sure there's no way for the cold air to get in.
If you can and it doesn't go against the theater policies, bring a blanket or a chair if you plan to sit.
If you think you'll be out for a couple of hours, it helps to have a buddy or make friends in line so you can make a quick run to a nearby restroom or grab coffee.
Don't do something dangerous. It's not worth it to stay out hours on a freezing morning. Sure, there will be less competition but you don't want to compromise your health and you won't enjoy the show later that day.
Do see if there's any word of mouth on how early other people who got tickets arrived maybe a week or two before you are thinking of rushing.
You might also need to plan ahead for altered schedules or delays in public transportation.