Two walkers had to be rescued from the summit of Ingleborough after travelling to the Yorkshire Dales from Rochdale.
Police say they had already turned numerous out-of-area visitors away from the beauty spot.
Despite the government advising the public to stay at home and stay local, the man and woman had travelled into the area to take some exercise.
Arriving ill-equipped for the climb, they got into difficultly at the top of the peak and had lost their way due to low lying fog, ice and snow.
Contacting the police at 4.30pm on Sunday , the worried walkers asked for help, as they could not locate the paths due to the failing light and the wintery conditions.
North Yorkshire Police called upon the experience and skill of the Cave Rescue Organisation to assist.
The volunteer rescuers scaled the peak and located the cold and shaken couple and brought them back to ground safely.
Speaking about this incident Superintendent Mike Walker said: “This couple were incredibly fortunate to have come through this experience without injury and be able to tell the tale.
“We very clearly advised members of the public this weekend to stay at home and when taking exercise, stay local to stop the spread of Covid. Quite simply driving miles and miles, out of your village, town or city to visit an open space is not a necessary journey and is not acceptable.
“Neither is arriving at a challenging walking location, inexperienced and unprepared in treacherous weather conditions. By making an irresponsible and ill-informed decision, the safety of others such as the Cave Rescue Organisation volunteers is also put in jeopardy and if any injury resulted, pressure placed upon already stretched NHS resources.
“Officers policing the Craven district have told me they were run off their feet this weekend, speaking to out of area visitors who had decided to ‘come out for a drive’ or had ‘come to look at the snow’.
“Thanks to these officers following the 4e’s, explaining the Covid regulations and encouraging visitors to adhere and return home, I believe a lot more accidents and rescues were prevented this weekend.
“It’s not just been challenging in the Dales either unfortunately. Across the county this weekend we have issued over 70 fixed penalty notices for breaches of the Covid regulations. On the coast in Scarborough we have again seen several house parties taking place, which have required our attendance.
“So again, I would ask people to really consider their actions and the decisions they are making. People should only be leaving home to make essential journeys and if taking exercise, staying local. In regard to socialising, people should not gather indoors with anyone who is not from their own household.
“Please think carefully about your actions and ensure you do not put yourself or others at risk or add any more pressure to already stretched emergency services.
North Yorkshire Police, Fire and Crime Commissioner Julia Mulligan said: “The rules and regulations are already very clear but there is a significant minority who seem to think they don’t apply to them.
“The message is simple – stay at home apart from for very specific reasons. Those reasons do not include taking a day trip to North Yorkshire from elsewhere or travelling to a different part of North Yorkshire if you live here.
“I fully support North Yorkshire Police’s approach which has always been to ask and engage with enforcement only as a last resort. But, I am clear – if they find blatant breaches of the law, they are absolutely right to take action.
“The vaccines being rolled out give us hope for the future, but for now each and every one of us needs to take responsibility for protecting our NHS and saving lives.”