Reg Peirson, a farmer in the village, had his landline switched to broadband last year.
He said while there were “pockets of mobile signal” in the village, he often struggled to connect, making the prospect of a power cut “quite scary”.
“It leaves me feeling extremely vulnerable,” he said.
“You hardly dare do anything in case you’re going to injure yourself, because you can’t summon help.”
Some mobile masts have back-up batteries or generators to keep them running for a few hours in the event of a power cut, but the one in Goathland does not.
Shelia Calvert, from Goathland Tea Rooms, said she felt it “shouldn’t be too difficult” to put something in place to keep the mast running for longer.
“You would think that would be an option – [power cuts] have a drastic effect at the moment because if people need help or need to call a doctor, they have no way of doing it,” she said.
For Ms Fearnley, a back-up mobile mast battery is “one solution” but one that would “only help those people that have a mobile phone”.
“There’s a lot of people of a certain age in our village who rely on landlines,” she said.
“The lights go off and it’s scary because you think ‘what if something happened right now in the midst of a storm’.”
She added her fear is “the infrastructure is not in place” to keep everyone in the village connected in a power cut, when the digital switchover is completed in 2027.
She said she worried that the lack of resolution so far was due to organisations “not having a true understanding about what lots of rural communities have to live with”.
She added: “I feel like something really awful would have to happen for people to really start listening.”