Short answer: Barnstaple barely changes in winter because it is a working town, not a resort. The Pannier Market is covered and runs Tuesday to Saturday, the museum is free, and the Tarka Line from Exeter runs all year.
This is the point of Barnstaple between November and March. The coastal villages half an hour west board up for the winter; Barnstaple carries on, because it serves the people who live in north Devon rather than the people who visit it.
A huge Victorian hall in the middle of town, Tuesday to Saturday, with independent stalls under a proper roof. It is dog friendly and wheelchair accessible, and on a wet January afternoon it is the best hour in north Devon.
The Museum of Barnstaple and North Devon sits by the Long Bridge and costs nothing — regional history, trades and wildlife, with a taxidermy section small children take to and a Victorian-style tea room. Closed Sundays, which catches people out.
The Tarka Trail starts at the station and is paved and traffic-free for its whole length, so there is no mud however wet it has been. That is a rare thing in a Devon winter and it is why this walk gets used all year.
Barnstaple is the end of the Tarka Line from Exeter. On a dark wet morning that beats driving north Devon lanes, and the trail starts where you get off.
Winter opening is where online listings are least reliable. Ring before you drive — several places here show as closed on Google and answer the phone perfectly happily.
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