North Yorkshire Police posted shared concerns on social media that people were travelling to Goathland and surrounding areas to enjoy the snow.
A message on Whitby Town Police's Facebook page read: "We are receiving reports that people are journeying to Goathland and the surrounding areas to sledge.
"This is in contravention of the current lockdown and Government guidelines around necessary travel and the public should not attend and risk a fine."
Under the current lockdown rules, exercise outdoors is allowed but is limited to once a day and should be "in your local area".
Goathland is famous as the setting for the TV series Heartbeat, and also as a stop on the popular North York Moors Railway. Its station became Hogsmeade Station in the first Harry Potter film.
Earlier this week two women in Derbyshire were fined £200 for alleged breaches of lockdown rules while on a walk at a remote spot around five miles from their homes in Leicestershire.