Scarves at their very most can be successful outfit accessories, but that's not what this post is about. It takes a very particular kind of man (usually a European one or a hipster one) to accessorize with a scarf. I'm not going to even try to instruct those who don't know how to "go there" on how to get there. What I will do, though, is advocate for every guy to get a scarf for warmth because if you do that right, you'll end up thanking me.
Consider a few things when going for a scarf, usually with respect to your coat:
color: The man in the photo above went for a bright color, and it works well. If you have second thoughts about something so bold, though, don't do it. It's best to have a scarf in a neutral--think black, brown (light or dark), or gray. You really only need one scarf, so if you're going to have one, make it in a versatile and safe color that will go with many coats. Only go bright if you're actually going to wear it, it goes with the rest of your outerwear and you have a not as bright option for backup.
pattern: Keep this to a minimum, and if you're going for a pattern, get one with colors that complement each other so the pattern stays muted. Go for the traditional patterns, plaids and checks, etc. You don't want people thinking you're wearing a girl's scarf. It's safest to go with a solid, but if you must have a pattern, think of what the most conservative CEO might go with on his suit socks.
material: Remember, this scarf is functional, so you're going to want it to be at least a decent thickness. No feminine pashmina or jersey scares here. You'll want to go with a nice wool or thicker cashmere if you're fancy. Texture is personal preference, but again, don't go overboard. Think about what's going to keep you warmest, what will itch and bother you the least and generally what you'll be able to stand around your neck for the times you spend outside in the cold.
detailing: Fringe or no fringe? And that's about all the detailing you should be considering. Again, this is personal preference, but just think about it before you buy, especially if it's going to show the way you wear it. There's no right or wrong answer to this one, but just consider your options carefully because cut off fringe is never a good look.
shape/size: Now think about how you're going to wear this. Looped around or doubled over and fed through or the double loop or the double feed through. Even if you only know one way to drape a scarf, make sure the width and length of the one you want works with that method. If you're only wearing it under you coat and close to your neck, you can go shorter, but if you want to loop it fancily or you want it to show over your coat, opt for one that's a little longer. If the one you want is online only, maybe go to a store and practice with one to make sure it will work for you.
There are lots of options out there, so just think about it, it shouldn't be too hard. And stay warm!