  We present deep continuum observations at a wavelength of 2mm centered on the
COSMOS field using the Goddard IRAM Superconducting Millimeter Observer (GISMO)
at the IRAM 30m-telescope. These data constitute the widest deep 2mm survey
to-date, reaching a uniform $\sigma\sim0.23$mJy beam$^{-1}$ sensitivity over
$\sim250$arcmin$^2$ at $\sim\,24''$ resolution. We detect four sources at high
significance (S/N$\,\geq\,$4.4) with an expected number of false detection of
0.09 sources, and five sources at $4.4>\,$S/N$\,\geq\,3.7$ with an expected
number of false detection of 1.65 sources. Combined with deep GISMO
observations in GOODS-N, we constrain the 2mm number counts over one decade in
flux density. These measurements agree with most galaxy evolution models tested
here, except those with large population of dusty star-forming galaxies at
$z>7$. Five GISMO sources have counterparts in (sub-)millimeter catalogs
available in COSMOS. Their redshifts suggest that all but one lie above
$z\sim3$. These four high-redshift ($z>3$) galaxies have $\tilde{z}=3.9$, SFRs
$\sim\,$400 - 1200M$_{\odot}\,$yr$^{-1}$ and $M_{\rm
dust}\sim10^{9.5}\,$M$_{\odot}$. They provide a relatively complete selection
($\sim66\%$) of the most luminous ($L_{\rm IR}>10^{12.6}\,$L$_{\odot}$) and
highest redshift ($z>3$) galaxies detected within our survey area by AzTEC at
1.1mm. We thus conclude that 2mm surveys favor the selection of massive,
vigorously star-forming, high-redshift galaxies. This is corroborated by
GISMO-C4, a source with a low false detection probability ($\sim\,6.2\%$), for
which the absence of a (sub-)millimeter counterpart supports a high redshift
origin ($z\gtrsim3$).
