Yes. The cold, specifically a couple good frosts, greatly increases the color change (and the sweetness). Here in northern California, we're having our (Owari Satsuma) Mandarin Festival right now....we haven't had frost yet, though, so there's still green rind on a lot of the fruit.

You could always try one of the fruits. They will often be ripe enough to enjoy, even though they're not fully colored.

Josh

Here's a story that tells a lot.. about a year after he had moved there from California, I visited my Brother in Tampa, FL. in January. He said to me, "you are the agricultural genius in the family... tell me what is wrong with my orange tree". I asked what was the problem; and he said my oranges are falling on the ground; but they won't get ripe.
I told him, they were surely ripe; and if he cut one open he would know; but they would likely NEVER get orange (what Californians recognize as ripe). So, depending on where you live and the climatic conditions there, your satsumas may never get truly orange. I would wait a couple more weeks and then start testing them one at a time until you see if they are really "ripe"