The Christmas market doesn’t know what’s hit it. At 8.30 on a mid-November morning Exeter is a whirl of white, a city half-blinded by tumbling flakes. Four market workers, caught out by this overly authentic addition to the festive decor, are busy shovelling the ground in front of the bao stalls and craft gin chalets. Above them, the cathedral’s medieval towers stand tall and cold in the heaven-filling flurry. Winter has arrived in Devon with bells on.

I’m here to catch a train to see some birdlife. A breakfast blizzard wasn’t part of the plan, but sometimes these things don’t go as expected. The city’s Queen Street has turned into a real-life snow globe – Narnia with sandwich shops – yet the little two-carriage train I’m catching trundles into Exeter Central bang on time. I find a window seat and settle in. Snowy rooftops roll by. Somewhere, an estuary lies in wait.

The Avocet line – named after the wader bird on the RSPB logo – runs between Exeter and the coastal town of Exmouth. It’s an epic rail journey, but not in the customary sense. “That’s £6.40 return,” says the ticket-seller. “And not a problem to break your journey in Topsham on the way back.” Built in 1861 as the Exmouth branch railway, the line covers a mere 11 miles, passes eight small stations and takes less than 30 minutes to travel end to end. For the second half of its length, however, the track hugs the shoreline of the Exe estuary – which is where the magic comes in.

The estuary is a fine spectacle in any season, more than a mile across at its widest point and stretching for eight miles. It’s sheltered by hills, lined by sandbars and sprinkled with shipwrecks. There’s year-round birdlife, in winter especially as more than 20,000 birds base themselves here to feed on the vast, nutrient-rich mudflats. Each muddy cubic metre, it’s said, provides the same energy as 14 Mars bars. The majority of avian visitors are seasonal migrants, drawn to this brackish low-tide buffet from their more northerly breeding grounds. For hungry waders, it’s the place to be.

But when the estuary looms into view this morning, north of Exton, the tide is high and it is sleeting. Through the mizzled train windows, I see a shape that might be a duck. By Exmouth, however, things are markedly brighter. Rain is spotting from the sky and estuary waters are lapping at the tide walls. The views are deep, damp and fresh. A stunt-team flock of overwintering dunlin, here from the Baltic, banks and turns above the water.

“I’ve been doing this since I was a boy,” Jake Stuart tells me. “It’s a way of life. I love it.” He is skippering today’s Stuart Line Cruise, a 75-minute sailing from Exmouth around the estuary. He’s the third generation of his family to work for the company, which was set up by his grandfather. Today, his passengers number me and a 40-strong coach trip from Sidmouth. Mince pies and whisky-laced hot chocolates do the rounds.

“Right now most of the birds are roosting,” Jake confirms on the PA. “They’ll appear at low tide to feed.” Taking a November pleasure cruise on a scenic inlet feels like getting one over on the calendar. There’s something out-of-time about the Exe estuary, too, something about its big skies and green hues that lifts you out of the digital age and makes life a little simpler. There are castles on the foreshore, boats in the harbours and oystercatchers on the sandbanks. But the day’s truest joys are still in store.

If, like me, you’re a bird-lover rather than a fully badged birder and your visit here coincides with a mid-afternoon low tide, here’s my advice. Bring binoculars. Buy a portion of salt-laced, vinegar-drenched chips for lunch and eat them on Exmouth’s Imperial Recreation Ground, watching the tide ebb and the brent geese appear. If you’ve got time, wander over to the esplanade to enjoy the wave-bashed views towards Torquay. Then catch the train back up to Topsham.

As I roll northwards, the estuary shallows are already alive with feeders: slow-stepping little egrets, mobs of stocky turnstones, a lone heron. At Topsham, with the sun now blazing overhead (did I dream the snowfall?), I start walking. This was once one of England’s busiest ports, its docks full of shipbuilders and wool shipments. Today, its streets are still lined with centuries-old pubs, while on its outskirts lies RSPB Bowling Green Marsh.

A 15-minute stroll brings me to a hide overlooking a reedy pool full of wigeons, teals and shelducks. Their chestnuts, greens and yellows are aflame in the afternoon sun. A happy half-hour later, I follow local advice to head to the Goat Walk (“for the views and the waders”), a raised, bench-dotted walkway directly above the mudflats. And here I stay until dusk, watching the winter feeders, a motley feathered crew variously arrived from Siberia, Scandinavia, East Anglia and the Arctic.

It’s amusing how the different species wade and forage. Redshanks nibble as they stride above their own reflections; bar-tailed godwits plunge almost eye-deep into the mud; and, thrillingly, 30 avocets sweep the mud with upturned bills. When I scan the distance with binoculars, the whole low-tide estuary is stirring with birds, tiny glowing silhouettes sprinkled like salt. Shimmering in the low sunlight, it’s beautiful.

“Curlews out there somewhere. Seen any avocets?” asks a passerby. I tell him yes. “Wonderful, aren’t they? They arrived yesterday, you know,” he says, then gestures along the shoreline. “I live just up there. Caused great excitement in our house.” Yesterday! I treat the fact as a gift. I cast my mind back to this morning’s snowstorm, then gaze again at the sunset mudflats, the sight a bona fide winter marvel. Sometimes, £6.40 can take you a long way.

Trip was provided by visitexeter.com and visitdevon.co.uk. Leonardo Hotel Exeter has double rooms from £88 B&B. Stuart Line Cruises offer winter sailings from Exmouth (including some dedicated bird-watching cruises) from £9.