Zaatari spokesman Wadah Hmoud said two days of heavy rains have flooded several areas of the camp. He said aid workers were struggling to replace tents with prefabricated housing units for the camp's 120,000 inhabitants.
Snow also battered most parts of central and southern Jordan, shutting down government offices, causing power disruptions, blocking roads and stranding motorists.
The snowstorm is expected to continue through Friday and possibly early Saturday, Jordan's Meteorology Department said.
In neighboring Israel and the Palestinian territories, the early snow surprised many.
In Jerusalem, schools cancelled classes and buses in and out of the city were not operating. Snow blanketed palm and cypress trees. Revelers threw snowballs along the walls of the Old City, while others built a snowman across from a U.S. Consulate building.
By midafternoon, the snow had turned to a cold rain, leaving Jerusalem streets slippery with slush. The main highway linking the city with Tel Aviv was closed till midday.
A light snow also fell throughout the West Bank, prompting officials to close schools and government offices for the day.
In the Gaza Strip, the Health Ministry said authorities evacuated 30 people to hospitals and moved others into shelters after heavy rains caused flooding and power outages.
Yousef al-Zahar, the director of Gaza's civil defense, said most of the water collecting pools were already filled with rain. He said a lack of fuel meant municipalities could not pump it out, so authorities were trying to close some streets with sand bags to channel water away from homes as a temporary solution.
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Associated Press writers Daniel Estrin in Jerusalem and Zeina Karam in Beirut contributed to this report.