I'm not sure what temperature will be there, "Western Europe" could be anywhere from Iceland, or Norway, or south Italy or Spain, or maybe just the UK, France, Belgium, Netherlands...
But no matter where, if it's regularly below freezing cold, I'm sure people outside for more than a few minutes would wear a hat of some sort (not counting high school kids who are cool enough they like frostbite). Here's a US chart about frostbite times (Temps in F though):
I've seen very few people wearing ear muffs anywhere (Canada, US, news from Europe), sometimes a headband, but more often a hat of some sort that at least partially covers their ears. There are always some people, either too cool, or unprepared, or with no feeling left, that just won't wear a hat or anything, but you do not want to copy them.
Maybe a toque like in Canada/us like these:
or a funny one like this
Or searching "french mens winter hat" found this surplus military hat, or a womens beret-type or warm looking hats:
I've tried wearing cheap earmuffs in -5C to -20C weather before, they were nearly useless, since like most people my ears stick out a little bit from my head and the earmuffs were flat, so didn't do much. Using my hands/gloves would be warmer. "Cupped" ear muffs might work, but even then your head still gets cold, so definitely go for a hat.