This will provide you a little extra protection from the elements and personally, I think hoodies make everything a little cooler, pun intended. If you are going to get yourself a nice formal Pea Coat in black or dark grey, try to find one with a hoodie built-in. I personally have a couple and this gives me the freedom to wear one no matter the weather. The great thing about these coats is that if you treat them well, they can last you for a while. Wool is a durable fabric and easy to clean so that should definitely factor into your choice for a new coat. I prefer the wool coat, they can be made thin enough to wear in the fall and early spring, but also can be made thick enough to tough the harsh winters in the Northeast.
You can also find these coats with a blend of fabrics and really it all depends on what you are most comfortable wearing. Traditionally the Pea Coat has been made of wool, and to this day, wool is the predominate fabric used for these stylish and utilitarian coats.