There are ways of taking advantage of the sun to dry your clothes even when it is cold. As long as it is sunny outside even if it is cold the clothes will dry on the line, it just might take a little longer then in the summer.
Also, a lot of people have sun rooms, these rooms are warm even in winter, put your line up in there, or sometimes the garage if it is warmer then outside.
Your clothes should never being dripping water, so there shouldn’t be a problem, if you clothes are still really wet when the wash is done, put them on a spin cycle once to get rid of the extra water. You should do this even if you don’t line dry, it will save time in the regular dryer also.
That is why I have a portable line, I can move it to the best spot for the job depending on the weather conditions.