Yes! Most natural materials have a relatively high emissivity at the infrared wavelengths associated with "typical" room / terrestrial temperatures. So in that sense, pretty much any material you might have (except for a highly polished metal that might have low emissivity) is suitable to get some cooling using the radiative cooling effect at night.
The fancier materials work is for two things: 1) selective emission which can allow the radiative cooler to get to a colder temperature than a natural material (many/most of which have relatively uniform emissivity), and 2) high solar reflectance at the same time, which can allow radiative cooling during the day as well.
The OP prompted me to check on Shanhui Fan's group[1], which had done some sub-ambient radiative cooling in sunlight[2], and I stumbled on this recent work:
A dual-mode textile for human body radiative heating and cooling[3]
Unless you go out in the sun. But yes, if you're hot indoors, wearing black clothing can help by radiating more heat. (And white clothing can help in the sun by reflecting more incoming radiation.)
The fancier materials work is for two things: 1) selective emission which can allow the radiative cooler to get to a colder temperature than a natural material (many/most of which have relatively uniform emissivity), and 2) high solar reflectance at the same time, which can allow radiative cooling during the day as well.