Depends on the conditions. Freshly paved interstate with clear lane markers, light traffic, daytime overcast skies with no rain? Maybe. Driving through a construction zones with painted-over lane markers at night, traffic cones knocked into the road, power out, and a police officer directing traffic at an intersection? No.
For mechanical reasons as well. My dad was a resident engineer at the Chrysler automatic transmission plant. He would send early production runs of transmissions to cab companies in San Francisco for stress testing...
If you take snow/ice out of the equation--admittedly a big if--it's probably fair that driving in at least many parts of SF are relatively challenging by US city standards for a person to drive in.
There are cities that are not in california, and some of them get snow.
Self-driving cars don't have to drive in snowy conditions; indeed, they don't have to drive in any conditions at all. It'd be nice if they could though.