Go read the trail journals of people who started in early Feb and note how quickly they disappear. Starting that early can result in very slow progress due to bad weather and short hours of daylight. It can also add a lot of extra expense. Many bail before long as being cold and wet 24/7 gets real old, real fast or they blow through their money due to all the days in town waiting out the weather to avoid being cold and wet.
A bivy is a big help in shelter situations as it will add a few degrees to your bag, will help keep the bag clean and dry since rain can blow into shelters and the shelter floors can get wet and muddy from people stomping around and hanging wet clothes in a futile attempt to get them to dry. They just drip water of the floor. Be sure the bivy has a breathable fabric top or condensation will kill you.
Since even that early in the season you still can't be assured of shelter space every night, you'll want a good sized tarp to put over the bivy when you have to camp outside the shelter.