I think the bigger problem is folks moaning about how silly, soft southerners have no perspective on weather. That attitude is entirely unhelpful, like all this nonsense about how nobody in the UK understands bad weather because of how bad Scandinavian countries have it. It's totally irrelevant.
There is less frequent snow and ice in London and the Home Counties than in the North and Scotland, no doubt. However, this means that people and infrastructure are both less prepared to cope when it does arrive; it's entirely reasonable and expected that this should be the case. The intensity with which infrastructure in London is used is also substantially higher, meaning that failures have larger impacts and more knock-on effects.
Much of the disruption that occurs during snowy episodes is a consequence of the actions of or statements made by the emergency services. Over the last few decades, it has become apparent to them, that road accidents, deaths and injuries spike during heavy snow episodes, the additional hazards and unfamiliar population make that inevitable. This of course drives up their workload at a time when they (like everyone else) find working more difficult. They are targeted to minimise accidents such and injuries, but they are not accountable for the loss of productivity or disruption to the economy. This means that they have a strong incentive to ‘advise against travel’, even when the impact on the wider economy might suggest a higher threshold (i.e. worse conditions) should be reached before issuing this advice.
This advice then sets off a chain reaction. School children for example may mostly have short walkable journeys, but a teacher coming 10 miles can legitimately take account of such advice. Faced with a likelihood of either too few staff members and possible last minute closure, schools are then incentivised to make a decision to close (possibly before the snow arrives) to avoid unnecessary journeys where other members of staff and parents discover that a school is closed on arrival. At this stage all sorts of people (including railway staff) face both advice not to travel and in many cases a need to provide unplanned child care and thus the working day grinds rapidly to a halt.
In addition to this, railway companies have also discovered that making a huge effort to operate immediately after heavy snow fall only succeeds in turning an abandoned day into a very disrupted one. They can be forgiven for asking, “why take the risks involved when heroic effort to keep things going will still look rubbish to the media?”
For those who say we used to do better in BR days, I would acknowledge that this is probably true, but at least a bit easier with one controlling organisation directing all staff (all hands to the pumps as others have said). The downside is that the people travelling or working to enabling travel were clearly put at a greater level of risk (taking account of the road journeys to / from the station) than is now accepted, while the incentives working on the multiple organisations involved in today’s rail industry give them little reason to make a huge effort.
(This is taken from a longer post to an earlier similar thread - see
https://www.railforums.co.uk/threads/snow-and-what-happens-if-it-comes.156954/page-4#post-3211171)