You may visit between December and February. The Rann of Kutch festival is also held around that time and the best days to attend the Rann of Kutch festival would be on any full moon day between the above mentioned months. You'll be treated with a great view of the Rann at night.
The best time to visit kutch is Nov to Feb. Rann Utsav is festival which is usually celebrated during this period.
Moreover look out for full moon days and dark moon and visit the kutch around that period. Because that is best time to have serene view of white desert.
Makar Sankranti is also a time when kite festival is celebrated in kutch which is also magnificent.
October end to mid of feb , that when is the run utsav is going on in Kutch and hence its a good time to visit Kutch. IF you could visit kutch during these months taking into consideration the full moon night, that would be even better.