Totally agree with paramount regarding higher ceilings making a difference. They can make a small place feel airy and open.
We’ve lived in a <1300 sf house with two small kids and were totally happy in it. Currently, our house is just over 2,200 sf, and we have three older and larger kids, and are exceedingly happy here, too.
We work and school at home, so are here pretty much 24/7. This takes up more space because the family room is a dedicated school/play room, but even after accounting for this, the house feels perfectly spacious and well-sized for our family.
As another poster already noted, you can have a well-designed 1,200 sf house that feels spacious and open, and you can have a 4,000 sf house that is poorly designed and feels totally claustrophobic. It's not the size that matters as much as the layout, orientation (sunny or dark), location/size/number of windows, ceilings, etc.
Nothing beats a nice place to play or hang out outside, IMHO, especially if there are nice trees and other types of attractive vegetation. Throw in great neighbors and a nice, walkable neighborhood, and the size of the house becomes less and less of an issue, especially in Southern California where you can be outdoors most days of the year.