Don't do this. Note that you are supposed to be aboard your BHX flight from Terminal C about 20 minutes after your flight from BWI docks at Terminal A. Even the slightest delay can blow this connection for you.

Ask CO to rebook you on an earlier flight to EWR. I don't connect through EWR at all if I can help it, and when I have to I allow a minimum 2.5 layover time, hopefully more. It's not just weather but ATC holds that can ruin your day.