It seems inevitable that you will be outside of a building. Even in a hellish swamp like the nation's capital, there will be times when you need to wear something in addition to your suit. That's a no-brainer for a Midwesterner like me, but I realized that there are people from warmer climates who may not be prepared for the mercurial nature of DC winter. You don't want to be out for coffee or waiting for a ride when it's blustery and below 40° without the proper attire. You won't be able to put on an air of confidence if you're literally shivering in your boots.
It may be hard to believe when you're wearing a suit jacket in the summer, but you will want to have outer layers in your wardrobe. You could repurpose your regular winter jacket and wear it over the suit. I've seen it done, but it never looks good. I would recommend that every closet include at least one formal coat. You don't need too many more than that, because you only wear them for part of the year and no one will think it's weird that you wear the same one every day.
Overcoat. An overcoat is basically a longer, oversized, and thicker suit jacket. It has a lot of the same design elements, like lapels, single and double-breasted variations, and a variety of fabrics to choose from. Black is the classic color that goes with anything, so I recommend you have one. Browns are also common and a solid choice, and some light patterning can often work. If you’re going custom, the fabric you want is in the 400 g range, ensuring it will be warm enough. It isn’t necessary to have a custom coat, as the greater lee-way with a coat means off-the-rack is generally viable. You could save the money for another custom suit.
Peacoat. You can think of the peacoat as an overcoat that's cut a little shorter, going around your waist rather than extending to the knees. The primary benefit of a peacoat is that it can go with more styles of clothing beyond the suit, while the overcoat looks best with a suit.
Trench Coat. Overcoats and peacoats are relatively heavy, and they’re not appropriate in that awkward phase of neither hot nor cold. The trench coat fills that niche. It's a quite billowy outfit, so heavy tailoring isn’t required. For colors, your standard is going to be the stereotypical light tan or brown, but you can make it more interesting. I would like a burgundy trench coat when the time comes to buy one.
Cold weather doesn't stop at your torso. You'll need something for your extremities to keep the wind and chill out. You'll need to protect your head, ears, and hands.
Hats. One of my weaknesses is my cold ears. The room feels several degrees colder after I’ve had a haircut. The problem is magnified outside such that I can get a headache absent protection. A problem with the more classic style formal hats—top hats, bowlers, and the like—is that they don't cover your ears and, therefore, don't provide much warmth. I opt for something knit like a beanie in a solid neutral tone.
Gloves. An underrated part of your kit, gloves ensure you can take your hands out of your pockets. The classiest gloves will be made of leather. I picked up my favorite pair on my honeymoon in Europe, and they're made of a buttery soft leather that is just a delight. Make sure they're lined with something like wool or the leather will provide little benefit. Other options made out of knitwear are acceptable.
Sunglasses. Never forget your sunglasses. That piercing sun through the clear and cloudless sky will interfere with your day. They don’t have to be fancy or extravagant, and I prefer simple and functional pairs. You'll want to make sure the lenses are polarized both to block light and filter out more UV rays. Without that protection, sunglasses will lead to greater eye damage because the greater pupil dilation will let-in more of the ultraviolet spectrum.