The famous ride, which was built in 1923 and is Grade II listed, stalled while passengers were still on it.
One passenger posted on social media: "We just stalled on Big Dipper in the snow and had to be evacuated.
"Great experience but freezing cold. Best front row ride ever."
In a statement, Blackpool Pleasure Beach said: "The Big Dipper came to a slow stop a short distance from the station platform.
" Passengers were all escorted safely from the ride to the platform a short walk (approximately 50ft) away and we thank them for their patience.
"The ride is reopening for the rest of the day and the park is open until 5pm this afternoon."
The wooden Big Dipper still has a huge following among roller coast fans.
It was extended in 1936 and was designated as a Listed Building on April 19 2017.
Blackpool usually escapes heavy snow but this morning was different, with large flakes soon coating the Blackpool area in a covering of snow.
It followed heavy wind and rain as Storm Eunice hit town yesterday and continued this morning.