While you may be dressing reasonably well for the chillier weather, you might not be keeping yourself warm enough. If you get achy shoulders, a tight neck or even a headache after being outside, consider if your neck and shoulders are exposed to the chilly air. Is there a draft hitting your shoulders? The temperature might not be cold but even a little chill can cause your muscles to reflexively tighten. This muscle contraction is the body's attempt to warm you by bringing blood to the chilled area.
I recommend having at least one favorite scarf, or even an assortment of scarves, at the ready. There are scarves for everyone: non-flashy, utilitarian scarves for those who are not into fashion and, of course, unlimited choices for those who want to add a little flair. There are lighter, cottony scarves that can be worn in the fall and spring, and heavier, warmer scarves for the winter. My advice is to make sure the scarf is comfortable, easy to work with and near your outside door. This will make it likely that you will remember and want to put it on.
Additional tips: Neck gaiters are an alternative to scarves. They are tubes of fabric that slide over the head. No wrapping involved. I have some that are thin and silky (made of "technical" fabric that wicks the moisture away; used in milder weather or for running) and some of thick fleece (easy to make your own if you have a sewing machine!). Also, if you keep a scarf or neck gaiter in your car, you will have it handy if you find the weather catches you off-guard.
I have been recommending scarves to my clients for years: men and women, fashion conscious and fashion averse. Many are now converts because they have experienced how scarves can alleviate upper body aches and stiffness.