It's a bit of a haul for you, but I used to live on Balboa Island in Newport Beach. Every year around Christmas time, they would bring in a snowmaker and make a snowy winter wonderland near the firehouse. All the kids would play in the snow. I think there was even enough snow to a bit of sledding. I just thought it was a cute idea -- especially for So Cal. I don't know if they still do it, but you might want to see if they do. I'll bet a toddler would enjoy frolicking in the snow.
There is a lot to see on Balboa Island too -- cute shops and restaurants along Main Street, the beach, Balboa Island Ferry, Balboa Fun Zone (there is a carousel there), Christmas boat parade at night. Parking can be a pain if you don't get there early, but if you plan to spend the day there, you can have lots of fun. I'm making myself homesick for Newport Beach now ;-)