'Shall we dance?'

These are the moments I like the most. It has snowed in New York. Two feet of it over the course of the night. A path has been cleared on 82nd Street between Lexington and Third. The path is just wide enough for two able-bodied people to squeeze through. It's a canyon really, a small canyon along the footpath, snow piled high on either side. On the street – a quiet street at the best of times, if anything can be quiet in New York – the cars are buried under snow. The telegraph wires sag. The underside of the tree branches appear like brushstrokes on the air. Nothing moves. Silence in the city. The brownstones look small against so much white. In the distance sounds a siren, but that is all, making the silence more complete.

I see her from a distance halfway down the block. She is already bent into the day. She wears a headscarf. Her coat is old enough to have once been fashionable. She is pushing along a silver frame. Her walk is crude, slow, laborious. She takes up the whole of the alley. There is no space to pass her.

There is always a part of New York that must keep moving – as if breath itself depends on being frantic, hectic, overwhelmed. I should just clamber over the snowbank and walk down the other side of the street. But I wait and watch. Snow still falls on the shovelled walkway. Her silver frame slips and slides. She struggles to keep going. I wish I could help her but there's nothing I can do. She looks up, catches my eye, gazes down again. There is the quality of the immigrant about her: something dutiful, sad, brave. Her gloves are beautifully stencilled with little jewels. Her headscarf is pulled tight around her lined face. She shoves the silver frame over a small ridge of ice, walks the final few feet and stops in front of me. "Shall we dance?" she says.

She takes off one glove and reaches out. She keeps the silver frame between us but for a split second we half-dance on the pavement. Then she lets go of my hand. I bend one knee and bow slightly to her. She nods back. She grins. She puts her glove on. Says nothing more, takes a hold of her silver frame and moves on, a little quicker now, around the corner.

I know nothing of her, nothing at all, and yet everything. She has made the day unforgettable.

Vladimir Nabakov once said that the purpose of story-telling is to portray ordinary objects as they will be reflected in the kindly mirrors of future years, to find in the objects around us the fragrant tenderness that only posterity will discern and appreciate in far-off times, "when every trifle of our plain everyday life will become exquisite and festive in its own right: the times when a man who might put on the most ordinary jacket of today will be dressed up for an elegant masquerade".

The snow keeps coming down in New York, with sublime indifference to the fact that it will melt tomorrow and its signature will be nothing but slush, but so what? As small and as anonymous as we are, these are the sort of moments that make us valuable. I wander home and end up calling my family. My mother answers the phone and tells me how cold it is in Dublin – eight below zero, flakes of snow coming down – and I think of how intimately connected we all eventually become, Dublin, New York, the woman on the street, turning the corner, always coming back.

Colum McCann's column for Round Midnight with Donal O'Herlihy on RTÉ Radio 1 (11.40pm) goes out every Tuesday night