We love the snow but hate the cold, and for almost 300 years Northern European winters were bitterly, catastrophically cold. Crops failed, there were famine riots and people died of hypothermia during the Little Ice Age. From the 16^th to the 19^th centuries, no population suffered at the hands of Old Man Winter quite as much as those in the Low Countries. Winters were long, life was harsh, but in Brussels Pieter Bruegel the Elder was singlehandedly inventing the winter landscape of our imaginations.

Crime fiction once lured you in with lurid covers acting like a B-movie poster or fairground barker, selling the promise of thrills within. The British Library’s new exhibition is disappointingly light on such disreputable fare, and much too brief. But within its self-imposed limits it manages to indicate the genre’s range, and illuminate some forgotten corners.

The first thing to say about Paul Elmsley’s portrait of the Duchess of Cambridge, which was unveiled yesterday at the National Portrait Gallery, is that it looks rather better in real life than it does in reproduction. That doesn’t make it a great painting, but nor is it a risible one. The soft-focused, Vaseline-smeared visage, framed by that undulating cascade of buoyant hair (it’s unfortunate how much this makes her look as if she's taking part in an ad campaign for shampoo) is more convincingly defined and skilfully modelled than it is when you see it on the screen.

For a man immortalised by his wails of rainy misery from the moors of Withnail and I, you would expect Richard E Grant to be very happy on the Riviera. He is, with the suave aristo manner of the Englishman abroad. Which is fitting for The Riviera: A History in Pictures, because the Riviera practically belonged to the Brits - we hivernots, winter escapers from northern cold - before the French realised it was there at all. And it came to their attention because artists from the Impressionists onwards went there.

"After such knowledge, what forgiveness?" TS Eliot’s line could well stand as an epitaph to Jacqui and David Morris’s troublingly thoughtful film about British photographer Don McCullin, whose haunting images of conflict across the world over half a century have defined our perception of modern warfare (though his range of subjects goes far beyond that).

The Mayan calendar recently suggested it was all over. It is now, almost. 2012 was, by anyone’s lights, an annus mirabilis for culture on these shores. The world came to the United Kingdom, and the kingdom was indeed more or less united by a genuine aura of inclusion. Clumps of funding were hurled in the general direction of the Cultural Olympiad, which became known as the London 2012 Festival, and all sorts leapt aboard. Just for a start, those opera companies who had been burning to perform a version of Vivaldi's L'Olimpiade could now finally proceed.

It was the year that everyone got just a little hysterical about Damien Hirst. That and the art market that made him. But that didn’t keep the visitors away from his retrospective at Tate Modern. The exhibition had more crowds than Wembley Stadium, or at least more than for any other exhibition in Tate Modern’s 12-year history (and possibly for any exhibition since Tate records began). It was cleverly curated (i.e. heavily edited) so it wasn’t half as execrable as some critics claimed it was (or said it would be before seeing it).

All roads start from Rome, and so it proves in this challenging exhibition put together from the holdings of the Royal Academy’s art collection, archives and library. It features 17^th-century Italian paintings – some of the grandest by the French artists who settled in Rome, and took inspiration from the surrounding campagna – brought back to Britain by the Grand Tourists who, in the midst of their various adventures, amassed substantial art for their stately homes.

The Royal Academy’s spacious white galleries at Burlington Gardens are flooded with mystic light and filled with New Age baubles. You are bathed in a trippy purple haze as you enter one gallery which contains a giant glowing pod. The translucent pod is meant to resemble an ancient monolith but instead looks more like an oversized Ikea lamp. The work derives its title, Tom Na H-iu II, from the Celtic “Tom na h-iubhraich” – a site of “spiritual transmigration”.

Carving in Britain from 1910 to Now is an accurate but unalluring title for what is a seminal show. The Fine Art Society is one of the oldest commercial galleries in Britain, founded in 1876 and still in its original building. Due to this longevity the FAS has unusual access to private collections, and an ability to mix the historic and contemporary to fine effect. The result here showcases an original anthology, simultaneously scholarly and commercial, a mix of loans and for-sale.