I can well believe this film is from 1963 as that year was a very bad winter with temperatures below freezing for several weeks. I remember my elder son starting school in January 1963 at the age of 5 and the road from our house to the school was a sheet of ice. My younger son was still in his pram (baby carriage in the States?) and my wife had great difficulty pushing it up the slope from the local shop to the road.
The great freeze and snow arrived with east winds on Boxing Night, 26th December and for the next 60 days "Britain became Siberia" (The Wrong Kind of Snow, Woodward and Penn.) The river Thames froze over. Millions of gallons of milk were wasted as tankers could not get to farms, some of which were cut off for two months. Diesel fuel froze. Snow drifted in some areas to depths of 43 feet/13 metres. Trains were stranded. The army used explosives to free ships from sea ice. (Facts from my own memories of that year and confirmed by the work cited above.)