The traditional Easter Monday event in Gawthorpe, near Ossett, has never been cancelled in its history. It has been run since 1963.
Heavy snow this morning led to concerns that the races - which see contestants carry a sack of coal on their backs - would be called off for safety reasons.
The children's race was cancelled and there were changes to the adult race programme, with several waves being reduced and consolidated and start times brought forward.
Just one veterans' race went ahead at 11.30am, followed by a women's race at 12pm and the men's event at 12.30pm.
Volunteers were clearing snow from the race route this morning.
Several competitors took to social media to express their disappointment at being unable to reach the village due to poor road conditions.
Vicky de Val said: "Not going to make it. I was registered in the first ladies' race. A couple of inches of snow, untreated roads and car issues - not a good combination."