There's no airport in the world that can carry on undisrupted during a heavy snow event, or storm-force winds, or dense fog, etc, for that matter. Heathrow and Gatwick have now invested very substantially in snow clearance equipment so that they can clear their runway as fast as can be reasonably achieved. But despite that, the unusual difficulty they suffer in comparison to most of the world's airports is that their capacity is so fully occupied that it is very difficult to make up any significant loss of runway time without some flights being cancelled. Nevertheless disruptive weather events at Heathrow and Gatwick are pretty uncommon, rarely persist much longer than a couple of days, and even if one happens this winter it is unlikely to be exactly when you are travelling.
I read forecasters predicting that it will be really cold and snowy this winter.
Those forecasters are charlatans. No genuine meteorologist would make such a precise prediction. The best a true scientist could do would be to say something like, "There is currently a strong el Nino underway, which is unlikely to resolve before winter. In 70% of previous El Nino events, a broad, but varying, area of NW Europe has experienced a cold, snowy winter". I say "something like", because in fact El Nino has no predictive effect on European weather at all. But I don't rule out the possibility some other weather cycle is in operation that might have some small predictive consequence for NW European weather. Nevertheless, at this distance, it could only be a tendency, nowhere near a certainty, and the localisation of it both geographically and in time, would also be uncertain.
What charlatan forecasters do, as much reported in the popular press, is make such precise predictions, and trumpet "there, told you so" on the small number of occasions that by chance they are right, knowing that the many previous times they were wrong will be forgotten.