Large numbers have been travelling to areas such as the Brecon Beacons, despite Welsh rules that say exercise should be taken near home and should be done alone or with your own household.
Wales is also closed to those from other parts of the UK unless it is for essential reasons such as work or providing care.
Powys County Council cabinet member, Councillor Graham Breeze said he had been shocked to see the pictures of large numbers of people visiting the Brecon Beacons to enjoy the snow.
“We all know that getting out and about is good for your mental health, but please stick to the rules and stay close to home," he said.
“We are at Alert Level 4 for a reason, because there has been a huge spike in Covid-19 cases which is affecting all parts of Wales. It is putting a huge strain on our health and social care services and is placing the lives of our most vulnerable residents at risk.
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“Powys has some beautiful places to visit but they will still be here to enjoy after the large number of coronavirus cases has subsided, while some of your relatives and friends may not if they end up catching this deadly disease.
“We need everyone to play their part and stay home over the days and weeks ahead – however tempting it may be to head to the county’s mountains, hills and lakes.”
"Please follow the national guidance and help keep Wales safe."
For the latest updates and information about coronavirus visit en.powys.gov.uk/coronavirus
In North Wales police have been patrolling areas of Snowdonia, sending people home who do not live in the immediate area.
Fines have also been imposed in some cases.
The Snowdon National Park Authority and mountain rescue teams have also warned day trippers to stay away.
The authority tweeted a message saying: "Although the snow does look pretty on the mountains the current Welsh Government guidelines say people should only travel if it's essential.
"No journeys of any significant distance should be taken, for example, just in order to exercise in the countryside or at beauty spots."