.............whereas in most other countries people just shrug their shoulders, put on an extra layer and get on with it, and the system doesn't seem to collapse like ours at the first sign of a snowflake.
I think that most places cope as well as you'd expect given how often they experience snow.
Do you remember that Paris was severely disrupted by snow just three weeks ago? It was forecast as 5-10 cm, and that was generally what they got - it was reported as 10-20 cm, but most likely that was just the deepest patches. What really caused the chaos was the usual one: roads full of traffic so the gritters couldn't treat them. They banned all HGVs from Paris, and a few roads closed - worst was the D118 from Port d'Orléans out to Versailles, where 900 cars were stuck overnight on high ground in the Foret de Meudon.
SNCF▸ Ile-de-France hoped to run well over half their trains, but some lines were much worse because so many drivers could not get in to work. They also had teams out defrosting points with gas torches, and generally kept the track open. But they did really have snow, so at the moment our railways do seem to be a bunch of - snowflakes?
Any snow immediately reduces the capacity of a road, so if it happens in a peak there are instant jams. We don't have any common understanding that, to prevent that, fewer cars should be on the roads. That implies a lot of people saying "I'll stay in/wait/cancel a meeting" so others can move around - and who would? And it's not much easier for "them" - some authority - to impose that, even if they could invent a way of doing it.
Of course once snow is deep enough to fill some cars' ground clearance, it's proper 4WD and other special vehicles only, even on the flat. Last time we had that - just - I could cope once the snow stopped on fresh snow if there were no other cars about, or on a treated road even if busy. But heavy snow mid-afternoon, or a few cars not coping with lying snow, and you might as well give up.