At least for butternut, when they're tan, they're largely ripe. If you leave the ripe fruit on the vine for a few more weeks, that mainly increases their storability. It should be noted that while freezing temperatures are certainly bad for the fruit, they can suffer "chilling injury" with temperatures below 50F. This leads to pitting in the surface, and increased incidence of decay in storage.

Tromboncino is usually used as a summer squash. That's the only way I've ever had it. So I'd pick it now rather than leave it to harden. Even large ones are delicious ime. They should keep fine in the fridge.

I think, but do not know, that a light frost will not harm flavor. It might not really get through skin to deep. So if that is true a light frost might be ok. I am curious if left on the vine will it "over ripen"?

I think, but do not know, that a light frost will not harm flavor. It might not really get through skin to deep. So if that is true a light frost might be ok. I am curious if left on the vine will it "over ripen"?

The issue is whether a light frost will kill the plant. It is true that winter squash are somewhat more frost tolerant than summer squash, but why take the risk?