I've never bred Palominos, so I'm just guessing based on the way the color looks and how it's described in the breed standard. The Golden color is Agouti-based, and I'm thinking most likely has the non-extension gene in the E series.
The New Zealand White is a bit of a puzzle. I've had only a little experience with outcrossing NZW's; the ones I bred carried the Steel gene. Steel is weird. It's a dominant gene, but apparently you generally get animals that look like Steels only when the Steel gene is paired with the normal full-color allele in the E series. Pair it with anything else (non-extension, harlequin, or another steel gene) and you'll get what looks like a (black) self. So there is a good chance that you'll get solid blacks or maybe steels from breeding your Pal to a NZW.
Red is based on the same Agouti/non-extension combination, the main difference being some modifier genes that dramatically increase the amount of red/yellow pigment in the hair. The most likely result of crossing a Pal with a NZR would be a shade of orange somewhere between that of the parents.
You said the Satin/Cali is mostly black - does that mean it's a Broken? I'd say the most likely result of crossing a Pal to a black self would be Chestnut, if the doe is a Broken, then some of her kits could be, too.
This one has me intrigued, because it's colors I haven't worked with before. Let us know how it comes out!