Last winter I placed a jasmine in south facing window near a baseboard heating unit, and another one in a unheat basement.
The condition of the one near the south facing window was going up and down. When I remembered to water it, it did fine despite it being bothered by spidermite. But when I forgot to water it for one week, it losed all the leaves and appeard to be almost totally dead -- except for one single green leaf. I left it there and continued watering it. Finally, it rebounded and recovered. Now, it is doing perfectly well outdoor. I intend to winterize it the same way in this coming winter.
The one in the basement didn't fare that well. It gradually losed all the leaves and it appeared as dead as a dead wood. Somehow in mid winter, it popped up with one tiny pale green shoot. But by the end of the winter, it was totally dead. In the spring, I put it out in day time and put it back indoor at night and doing this for one week. But this was of no use because it was DEAD.
I am not saying that my experience is applicable to other people. But at least for me, putting it in a south facing window not far from a baseboard heating unit and watering it periodically is a better bet than placing it in a basement.