Why are Zucchini's refrigerated, but not acorn and spaghetti squash?
The short answer is that they are different types of squash, although both are squash.

Zucchini is a summer squash, which has soft flesh and a malleable rind.

Both acorn and spaghetti squash, much like pumpkins, are winter squash, with harder flesh and a tough rind.  If cured, they can be stored for months at cool root cellar temperatures, and for a reasonable amount of time at regular room temperature.