Check the stems. Are they just limp, or are they decaying at the base? And check the soil. Is it dry all the way through? What I suspect to be the case is: Cacti need water too, just not as much. If the mix is dry all the way through, that is too dry. If that's the case, give it a good watering right away. The limpness, if there are no signs of rot, is simply wilt from moisture lack. Keep the mix barely moist throughout winter, not bone-dry.
Also, cacti need smaller containers. Planting in a container that size will lead to different problems, like dry center, where the original soil remains dry even after watering. A pot 1/4 that size should be plenty. If the bases of the stems are rotting, there is nothing you can do but take cuttings from the remainder, or graft them onto new rootstocks (easier than it may sound). Also, the plant seems to have leaned towards the window. In warm temperatures (70 degrees F. and higher), desert cacti need full sun for best health. If you can't provide that, I'd suggest that you look into a lighting system that will work for you.
As a note, cacti do best with a winter rest period, when you let them dry most of the way, but they need lower temperatures (between 55 and 65 degrees F.) and shorter, but not too much less intense lightwise, days in order to go dormant properly. If you can't provide the cooler temperatures, don't dry the plant out. It will wilt.
If the plant is healthy, I'd repot it back into a smaller container as well. Here's what the Reader's Digest book 'Success with House Plants' (highly recommended, by the way) has to say about the potting requirements of cacti:
In the wild most desert cacti have a widespread root system. The roots of a plant 6 inches tall can extend, just below the soil surface, for a square yard. This enables them to collect a good supply of surface water in the form of dew. The roots of plants grown in pots are much more compact and the potting mixture must have especially good drainage in order to avoid the risk of rotting. Apart from the drainage requirement, desert cacti have no special potting-mixture needs. A suitable mixture consists of about one part of coarse sand or perlite to two parts of either soil-based or peat-based mixture.
This correlates well my my personal experience with the cacti. The book then goes on to describe the repotting process in good detail.