Spider plants like bright, not direct sun.  As the path of the sun changes in the winter, it may not be getting as much sunlight as it likes. 

However, the common reason for fading, limp leaves is under-watering. You can let the top of the soil dry out (even much lower), but the pot's soil needs to be at least half moist.

Also, in the winter house humidity goes way down. Spider plants like humidity.  Place it on a tray of pebbles in water, or let water in the saucer evaporate up around the foliage. 

In order to have 'babies', spider plants must be mature enough, which sometimes takes years.  Some believe the plant must be root bound. Here are more possibilities: https://www.gardeningknowhow.com/houseplants/spider-plant/getting-spiderettes-on-plants.htm 

Ellen