OK. Well, unless you want your jalapeño plant to continue to produce during the winter, you could leave it outside as long as temperature stays above mid-20's which will kill the roots. Peppers are frost sensitive so the leaves will die at low 30's, and the more tender upper stems/branches will die off, but the hardened lower stems and branches will grow new shoots in spring/when warmer.
But you have to decide early on whether to overwinter in dormant state since the plant needs to adjust to the colder temps to properly phase into the hibernation mode.
It sounds like you are growing one plant in a container -- is that right? If so, be sure to give it a good sized pot to grow in for the season to keep it healthy.
I have to bring my peppers indoors for the winter since it gets too cold outside. I root prune and trim the branches to just above the green immature fruits and flower buds to pot them up (or just stick them in doubled up grocery bags). In the house, my windowsills can get as cold as upper 40's to mid-50's but while the temperatures are in upper 50's to mid-60's, the jalapeño will continue to bloom and set/mature fruits. I put them in SE-facing window with window treatments open during the day, and provide supplemental light that stays on from morning to bedtime.
They seem to take a break around winter solstice -- maybe day length, but it gets super cold around here late Dec to mid Jan -- peppers starts growing (lots of) new shoots after February and start blooming and setting fruits by spring.
Watch out for aphid infestation. If you see ants, they are bringing aphids to pasture on your plant.
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