I found a mature caterpillar on my parsley. It formed its chrysalis about three weeks ago in late September, on a twig in a plastic container.. Do you think it will stay in until spring, at this point? I tied the twig to a branch of my dogwood. Is this the best thing to do with it?

Yes Sally it will overwinter and hatch in the spring

Thanks, Ronnie!

One of my swallowtails has been in chrysalis for a couple months now.
I have put he and his mesh enclosure in our unheated, detached garage.
One advantage to doing what you did is that the chrysalis will be exposed to natural precipitation.
I've been misting mine a couple times a week so it doesn't dry out too much.