NOTE: I live in CT..it does get cold here! If you live where it does not get so cold, then this advice may not be for you!:

If it does gets cold where you live (and I don't mean that "It's only 60 degrees out today! It's freezing!" stuff), your head protection can make a difference in how you feel...and a cold head and/or ears is no fun!

I happen to concur with Mpehtameme's choice of the full-face helmet. If you run flat/straight bars, they work just fine! And, they keep the weather off without any problem. And, to deal with the "gaps' there are? You may not need to most days, but if it gets cold enough a thin balaclava will fill in any "gaps" without making the helmet too tight. An advantage is that these helmets have few, if any, vents, so you don't end up fooling with "hole stuffers"...or headbands or ear covers, which can be a pain to use. (The helmet itself provides the ear insulation!) Also, a good full-face helmet is designed to work with full goggles, such as ski goggles, since goggles of a very similar style are used in BMX and downhill MTB racing.

The problem that people seem to be thinking of here--the "roadies" especially-- comes when using "drop" bars...then the full-face won't work! (The chin guard and/or visor blocks part of the view when you are lower than the "hoods"...and can be a problem even on the "hoods" if the bike is built to allow for a "race-like" rider position.) The best solution here would be the BMX-style "half helmet" that fatbat has in mind, without the chin guard. No visual field problems then! You will need to fill in the few holes they have to keep the weather and wind out, as well as use a balaclava/ear band almost all the time, though.