Generally speaking, the opposite happens in the central and eastern Pacific during La Nina because the cooling process limits the amount of heat and moisture that rises into the atmosphere. It's sort of like turning off a fire hydrant. In the fall and winter, the colder waters also contribute to the development of high pressure in the North Pacific. That high pressure pushes the storm-bearing polar jet stream unusually far north, sending it through British Columbia and the Pacific Northwest. That means that fewer storms dive down the California coast, into Orange County.
Some storms do manage to drift south.
But Southern California is typically drier during La Nina winters. The Western Regional Climate Center says nine of the past 12 La Nina winters in Southern California were dry, three were about average and none was wet. La Nina also causes the fall and winter to be windier than normal in Southern California. That's because the polar jet stream periodically dives south along the Rocky Mountains, into the Great Basin states. This flow causes high pressure to build west of the Rockies, generating dry Santa Ana winds that explode off the Mojave Desert into Orange County.