It depends on how "one" is used. Sometimes, but not always.

You have to say "each one of them" or "every one of them"

Both "Each one was happy" and "Each one of them was happy" are correct, but you can't say, "Each one them was happy." When "every one" is used in the same sense as "all" (which it usually is), then it's written as a single word, as "everyone."