Nature's Power
Despite the fact that this poem takes place in one of the world's busiest cities, the snow manages to turn it into a kind of pastoral paradise. This effect is so intense that, except for the title and a few sly references, it's easy to read the poem and not realize it's set in London or in any city at all. Its first lines describe a city overtaken by nature, devoid of the most defining and important part of urban life: people. When the people wake up, their actions aren't dictated by the conditions of city life. Instead, the snow, a natural phenomenon, takes charge of their day. It is the snow's brightness that wakes them, and the schoolboys who play in the snow are momentarily able to enjoy the sensory excitement that pastoral, rural life might provide. Even the city's workers, who cannot actually change their routines, feel completely different in the snow—as if their normal concerns are simply unimportant. Overall, Bridges suggests that nature is far more powerful than human creations like cities, easily making them seem frivolous.
Illusion
The poem's closing line states that, simply by noticing the beauty of the snow, London's workers actually break the "charm" of urban, modern life. In other words, city life and its attendant concerns are mere illusions. They are persistent ones (these men still go to work, even if it's just a "charm") but they're illusions nevertheless, sustained only as long as nature doesn't decide to make them totally impossible. The fact that the "charm" is broken not by action, but by an internal process of observation and appreciation, suggests that the illusion is primarily sustained via widespread belief that it is real. That is to say, city life isn't real the same way that the natural world is, (according to this speaker) but it is able to sustain an almost supernatural appearance of realness provided that Londoners collectively maintain faith in its importance. When they lose that faith, perhaps through contact with the natural world, it doesn't matter whether London and urban life persist—they lose the appearance of realness and are shown to be illusory.
Childhood
The snow brings a transcendent excitement to a group of London schoolchildren, who are able to play outside in a way typically associated with rural rather than urban childhood. The snow, in fact, gives them a kind of renewed innocence. They are able to treat all of their senses with new excitement, from taste (by eating the snow) to touch (they make snowballs until their hands freeze)—like very young children still enamored with every part of the world. The description of the schoolboys suggests that, while urban life is disruptive to childhood's wonder and purity, the natural world nurtures these attributes of childhood.