According the Rebbe the Tzemach Tzedek, (Ps”d 3), there is one opinion which holds that the Mitzvah of wearing Tzitzis has been performed at night (even if) the garment with the Tzitzis is a garment used for day wear, while ‘night garments’ such as sheets and blankets, are not in the category where one is obligated to attach Tzitzis to them, thus the Mitzvah of wearing Tzitzis is considered a time-controlled positive Mitzvah that women are not obligated to perform.
If one uses bedclothes during the day, there is an opinion that one is obligated to attach Tzitzis to them. The Alter Rebbe in his Shulchan Oruch (18:5), writes that according to this one should attach Tzitzis to the bedclothes, because people get up when it is already daylight. The Alter Rebbe concludes by suggesting that one rounds off one of the corners of each blanket (this is regarding woolen blankets, and in the Alter Rebbe’s Siddur he writes the same regarding all kinds of blankets), in order not to become obligated to attach Tzitzis.
It is desirable to wear Tzitzis during sleep at night.