Recommend a Snood

For me, these are possible pros. NB I'm more of a functional cyclist, cycling as transport to work, shops, visit friends etc so can't speak for long-distance or sport use so much.  If you are on the way to the shops, it doubles up as your face mask when you arrive. A breathable one with a UV filter made from eco-friendly fabric will keep your neck warm without getting sweaty and can be hi-viz if you want some extra-visibility in the dark.  I'm sure there are other pros and cons depending on how and when you cycle. I have two from Buff, which if you buy from workwear stores online are much cheaper than buying from cycing stores. 

Pros: lightweight, stuffs in pocket, more useful than a beanie or cap (though I wear a cap when it's raining or particularly cold) and cheap. Also not cycling-specific.

Cons: none that I can think of.

It's neckwarmer /draught excluder for the neck that can also be used as an ear warmer, an under-helmet headwarmer or a face covering. There are videos online showing the many ways they can be used.

So-called 'genuine' Buff branded are overpriced, they all do the same thing. I have one I won as a raffle prize, plus a cheap camo from ebay my daughter has purloined and an Altura. The Altura is quite long so used double layer and keeps the wind out very well.

I have a thick motorcycle one (those days are probably gone for me  ) but I'd only consider wearing to cycle it if the temperature was some way below zero.