Although 70% of the stars in the Galaxy are M-dwarfs, thermal emission searches for cold debris disks have been conducted mostly for A-type and solar-type stars. We report on new lambda=1.2 mm continuum observations of thirty M-dwarfs, using the MAMBO-2 bolometer array camera at the IRAM 30 m telescope. For a statistical analysis, we combine these data with our prior SCUBA and MAMBO-2 observations of 20 other M-dwarfs. Our sample consists of M-dwarfs in moving groups, with relatively young ages, and of nearby M-dwarfs with unknown ages. Only one cold debris disk (GJ842.2) was detected significantly. We compare the implied disk abundance constraints with those found in two comparable submillimeter surveys of 10 to 190 Myr old A- and FGK-type stars. For the 19 youngest (ages less than 200 Myr) M-dwarfs in our sample, we derive a cold disk fraction of 5.3^+10.5_-5.0%, compared to 15^+11.5_-11.5% for FGK-stars and 22⁺³³_-20% for A-stars. Hence, for this age group, there is an apparent trend of fewer cold disks for later stellar types. Although its statistical significance is marginal, this trend is strengthened by the deeper observations of our M-dwarf sample. We derive a cold disk fraction of