The accident happened as the women were heading early Thursday to St. Catherine's Monastery at the foot of Mount Sinai, said Col. Ahmed Said, the monastery's police chief.
Ambulances rushed to the scene and the injured were transported to hospital in the Red Sea resort of Sharm el-Sheikh.
Said says two of the women are in critical condition. Their Egyptian driver was unharmed.
Road accidents are common in Egypt, which has one of the world's worst traffic safety records. Snow however, such as that brought in by the fierce winter storm to hit the region this week, is a rarity.
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