SAN JOSE, Calif.—Record-low precipitation in 2013 has worsened California's drought, draining reservoirs, forcing farmers to keep fallow thousands of acres of fields and leaving some ski resorts high and dry during the busy holiday season.

Urban and agricultural customers, including Southern California's huge Metropolitan Water District, have been told by the state to expect to receive this year, on average, just 5% of the water they historically request, after a year in which rainfall totals hit record lows in many parts...