More than once I have been in that mile long line as scores of flights are ground due to weather. Here are my tips:

Dial the reservations number while waiting in line. Have the phone agent make new flight arraignments, then once you get to the front of the line you will already have arraigments and they can simply print your new boarding passes. If you wait till you get to the front of the line those new flight options might be gone.

The other bonus of calling before you reach the front of the line is you will already know if you will be getting out that night or if you need to ask for hotel/food vouchers.

Go to the shortest line, not just the line at your gate. Go to the service desk, the club lounge if you have membership, I've even gone back to the pre-security ticketing area to save time in line.

If you get the chance to check the weather the day you are flying and you know it might be a factor have a re-route option in mind on your preferred airline ready to suggest if your flight is canceled.

If you do get stuck for at the airport for a while or overnight don't be shy in asking for meal vouchers, hotel vouchers, a day pass to their club lounge, phone cards, overnight toiletry kits, etc.

Be nice to the people helping you, it can make all the difference in getting that hotel voucher even when they don't have to give it to you when your flight is canceled due to weather.