The first proper cold snap does something to a kitchen. The oven goes on earlier, the windows fog, and the butcher starts using words like brace and haunch as though autumn were a person who had finally arrived. Game season is upon us: partridge since the start of September, pheasant from the first of October, grouse since the Glorious Twelfth back in August. Which leaves the only question that really matters once the roasting tin is out. What are we going to drink.

Game divides people, usually along the line of whether they have ever had it cooked properly. Done well, it is the most rewarding thing you can put in an oven all winter: leaner than farmed meat, darker, wilder, tasting faintly of the hedgerow and the wood it came from. Done badly, it is dry and liverish and puts a person off for a decade. The wine cannot rescue a badly cooked bird. But the right bottle beside a good one is among the great pleasures of the colder months, and it is not remotely hard to get right.

Game has quietly become the thing to order out, too. Come autumn the good London tables put it front and centre, from the whole bird on the bone at a proper St James's dining room to the venison ragu that lands on every neighbourhood bistro's specials board the moment the clocks are due to change. Cooking it at home is cheaper, every bit as good, and gives you the run of your own rack. Which brings us straight back to the bottle.

The trick is to stop thinking about game as one thing. A roast partridge and a slow-cooked haunch of venison have about as much in common as a whisper and a handshake. Match the wine to the bird, or the beast, in front of you, and reach for something with savoury character rather than sweet, sunny fruit. Game is a savoury, earthy business, and it wants a wine that speaks the same language.

First, feather or fur

Everything starts here. Feathered game (partridge, pheasant, grouse, wild duck, the odd woodcock for the brave) tends towards elegance and a fine, gamey savour. Furred game (venison above all, but also hare and rabbit) is denser, darker and more muscular, often cooked long and slow with juniper and a bottle of red in the pot. The feathers want a wine of finesse. The fur wants a wine of muscle. Get that one division right and you are most of the way home.

The birds: partridge, pheasant and grouse

For feathered game, one grape sits head and shoulders above the rest, and it is Pinot Noir. Red Burgundy and a roast game bird is one of those pairings that feels less like a match than a reunion: the wine's red-fruited lift, its undergrowth-and-autumn-leaves savour, its silk where a bigger red would bring grip. It flatters the bird instead of flattening it.

For a proper occasion, a grouse well hung and roasted rare, reach for a savoury, structured village Burgundy. Domaine Robert Chevillon's Nuits-Saint-Georges Vieilles Vignes is Nuits made flesh: dark cherry, iron, a breath of the forest floor, the sort of bottle that seems to have spent all year waiting for a plate like this. Midweek, when the bird is a simple roast pheasant and the occasion is only Tuesday, an honest grower Bourgogne like Domaine Alain Jeanniard's Quintessence does the same job in a quieter register, and does it beautifully.

Partridge is the lighter, sweeter bird of the three, and it takes happily to something with a touch more juicy fruit. This is the moment for a serious cru Beaujolais. Daniel Bouland's Morgon Bellevue Cailloux is the Gamay that converts the sceptics: bright, peppery, faintly wild, with the structure to stand up to the bird and the charm to keep the table talking. At under thirty pounds, it is also one of autumn's quiet bargains.

Venison and the furred game

Now the wine needs shoulders. Venison is dark, lean and faintly sweet, more often than not braised or roasted with juniper, bay and a good slug of red in the pot. It can take real structure, and the classic answers all involve a little age and a lot of savoury depth.

Nebbiolo is the wild card that always wins. A Barolo, all tar and roses and fine drying tannin, has an almost gamey, autumnal quality of its own; it meets venison as an equal and never blinks. Prunotto's Barolo is the rare example you can open now rather than in a decade, generous and ready, with exactly the tannic backbone a haunch demands. Northern Rhône Syrah pulls off the same feat from a smokier angle, all black pepper and cured meat and violets, if you would rather stay in France.

And then there is claret, the old reliable. A mature red Bordeaux, with its cedar and blackcurrant and firm Cabernet grip, was more or less built for a rich, slow-cooked haunch. Château Batailley, a dependable Pauillac from the classed growths, brings the gravel-and-graphite seriousness that turns a big roast into an event rather than a Tuesday.

Those two between them cover the whole season: the Burgundy for anything with feathers, the Barolo for anything on four legs. Keep one of each in the rack from October onwards and you will not be caught short when the butcher hands you something wild.

A handful of rules that never fail

First, hanging matters. The longer game has been hung, the stronger and more mineral it tastes, and the more wine it can take: a lightly hung young partridge wants a gentler bottle than a bird that has ripened for a fortnight. Second, weight for weight, as ever. Delicate bird, delicate wine; muscular beast, muscular wine. Third, decant the older reds. A mature Burgundy, or a Barolo with a few years on it, wakes up beautifully after an hour in a jug, and game is patient food that rewards a little ceremony.

Above all, do not overthink it. Game is festive, generous, faintly ancient food, and it suits being drunk around rather than analysed. A good bird, a good bottle and a table in no hurry to clear: that is the whole of the ambition.