Organisers said the front-runners were on the day's third climb when the race jury decided it was too dangerous to continue the hilly 168-km stage from Cusset to Mont Brouilly in the Beaujolais wine region.
Television images showed concerned riders talking to each other as the snow fell on them, before heading back to their team cars with about 70km remaining.
Alexis Gougeard (AG2R), Alexy Lutsenko (Astana), Laurent Didier (Trek-Segafredo), Thomas De Gendt (Lotto Soudal) and Jesus Herrada (Movistar) were leading the race by 3min 30sec when organisers decided to call it a day.
The race was in the third climb of the day, Col des Echarmeaux, when it was judged too dangerous to go ahead.
The points collected in the intermediate sprint of Chauffailles and in the first two climbs of the day, Cote de Verney and Cote de Chateauneuf will be taken into account for the fourth stage to Romans-sur-Isere.
"The road was extremely slippery and the safety was no longer guaranteed. We are sorry. That's Paris-Nice. We promise we'll come back to Mont-Brouilly. It's a pity but the riders will start again tomorrow from Julienas," ASO cycling director Christian Prudhomme said.
Overnight leader Michael Matthews (Orica-greenEDGE), who won the second stage to go with the prologue, leads Tom Dumoulin (Giant-Alpecin) by 14 seconds, with Cannondale's Kiwi Patrick Bevin in third place, 19 seconds off the pace.
The race ends on Sunday in Nice.
FDJ riders stopped during the third stage of Paris-Nice (Getty) Source: Getty Images
BMC's Philippe Gilbert (upper respiratory infection) and Pierrick Fedrigo (bronchitis) of Fortuneo–Vital Concept pulled out before the stage. Arthur Vichot (FDJ) who was dropped early on, later abandoned with gastric problems.
"I really love this race so it is disappointing to have to stop racing," Gilbert said.
"But I have one of my biggest goals for the season, Milan-San Remo, around the corner and in order to perform well there I need to fully recover from this illness."
Thursday's fourth stage is a 195.5-km trek from Julienas - another region specialising in light red wines - to Romans-sur-Isere at the foot of the Vercors mountain range in the Alps of southeastern France, and features three small climbs.
