People have been flocking to Brown Clee, between Ludlow and Bridgnorth to enjoy walks and, most recently, the winter snowfall.
But after complaints by local people and concerns from the tenant farmers the Burwarton Estate has now put up signs saying the area should only be used by those who live in the nearest parishes.
Will Worthington, forestry foreman for the estate, said that this year had seen a huge increase in numbers visiting Brown Clee, the highest of the South Shropshire Hills.
"We normally welcome visitors and it saddens us to have to do this," he said.
"We all need to get outside for our mental health."
"The normal volume of people who come to walk on the hill isn't a problem but the volume has increased dramatically."
He said there had been complaints from tenant farmers about gates into fields being blocked by cars and also gates being left open.
"It has been causing problems for farmers who need access to feed their livestock who find their way has been blocked by people going sledging. Also we have had reports of lifestock being misplaced because gates have been left open."
Mr Worthington said that the number of cars on local lanes had got so bad that it had become dangerous, potentially blocking the access to local homes and the hill itself for emergency services.
He said that during the current lockdown the estate wanted to give residents peace of mind.
"There have been no clear guidelines from the Government about how far you can travel to exercise, simply that you should stay local, your own village, town or city. We looked at the areas where we thought people would be able to walk from when we drew up the list of parishes."