Shakespeare plays are like London kettles. Over time, they calcify. Polly Findlay's As You Like It, the first at the National since 1979, applies descaler. All those accumulated tics and tropes dissolve, restoring the play's real flavour. It is, in short, one for the history books.

Often played as Shakespeare's balmiest comedy – summery fare – Findlay shunts the play into "winter and rough weather." Seasonal switching is the National's way: its last Twelfth Night was autumnal; its Midsummer Night's Dream, a muddy puddle. The aim is to push past all that knockabout business – you get that elsewhere, without £17 million subsidy – and find the play's soul instead. Slowing the speech and dropping the be-dum-be-dum-be-dum laughter lines, Findlay lets you hear the text anew, in full. Who knew, for instance, that death cropped up so often? More than 50 mentions in all.

Hence, the wintery Forest of Arden: harsh, bitter and exposed. It is a million miles from Duke Frederick's court/corporation: an office with regulated greenery – a bonsai on every desk for mindfulness' sake – and a synthetic, upbeat colour-scheme. (Very London 2012.) Employees snatch lunch al desko, and the wrestling match – Leon Annor's Charles is a large luchador – becomes a Wolf of Wall Street-style reward. Here, happiness is all. (It boosts productivity.)

Not so in Arden, where Duke Senior's gang huddle round tiny fires like survivors in a Cormac McCarthy novel. Lizzie Clachan's forest is a thicket of desks and chairs, hanging like tangled trees, wires like vines. It could be furniture falling from the Twin Towers, an office exploded apart. It seems deep and endless and hostile. It's alive as well: a shadowy chorus sit in the trees, chattering and pattering, twittering and howling. Orlando Gough's haunting choral music drifts in and out. Rosalind and Orlando (Rosalie Craig and Joe Bannister) stride in like one-man Millets outlets: protected against the elements and braced for every eventuality.

This is Jacques' territory. This might even be his play, not Rosalind's. Paul Chahidi shuffles on like a man who's lost his lot in life: an unshaven divorcee or a freshly-fired exec. He uses the forest floor as a psychiatrist's couch and drifts listlessly through the forest, in search of fools to pass the time. What's melancholy if not depression? Chahidi lets you hear the horror of a life ‘sans taste.'

All this taps into something deeply contemporary – the desire to throw off the trappings and comforts of modern life. Alan Williams's Corin becomes truly enviable: his simplicity, a strength; his slowness, a virtue. At one point, his flock fill the stage, the entire cast in white wool jumpers, on all fours, chewing the cud. Findlay gives him the priest's part too, entwining spirituality and nature, as Clachan's forest becomes a kind of cathedral.

There's more. Findlay adds a feminist slant. This foreboding forest stands for the harder side of love, and it's full of men chasing women. Rosalind's defence is not to run, but to hide, disguised as a man. While Craig plays down the comedy of that, she plays up the cowardice. Her Ganymede is a betrayal – not just through the casual misogyny, but through its deception. She is not a vintage Rosalind – she lacks the swagger to win so many hearts – but she is an interesting one, especially next to Bannister's anxious, millennial Orlando.

There have been funnier As You Like Its, for sure – despite the total brilliance of Patsy Ferran's fidgety, clumsy-thumbsy Celia – but it's rarely as rich or as revitalised as this. Go.

As You Like It runs at the National Theatre until 5th March. It broadcasts via NT Live on 26th February.