Debris disks are believed to be related to planetesimals left over around stars after planet formation has ceased. The frequency of debris disks around M-dwarfs which account for 70% of the stars in the Galaxy is unknown while constrains have already been found for A- to K-type stars. We have searched for cold debris disks around 32 field M-dwarfs by conducting observations at λ=850µm with the SCUBA bolometer array camera at the JCMT and at λ=1.2mm with the MAMBO array at the IRAM 30-m telescopes. This is the first survey of a large sample of M-dwarfs conducted to provide statistical constraints on debris disks around this type of stars. We have detected a new debris disk around the M0.5 dwarf GJ 842.2 at λ=850µm, providing evidence for cold dust at large distance from this star (∼300AU). By combining the results of our survey with the ones of Liu et al. (2004Sci...305.1442L), we estimate for the first time the detection rate of cold debris disks around field M-dwarfs with ages between 20 and 200Myr. This detection rate is 13+6–8% and is consistent with the detection rate of cold debris disks (9-23%) around A- to K-type main sequence stars of the same age. This is an indication that cold disks may be equally prevalent across stellar spectral types.