We present the characteristics of 2 mm selected sources from the largest Atacama Large Millimeter/submillimeter Array (ALMA) blank-field contiguous survey conducted to date, the Mapping Obscuration to Reionization with ALMA (MORA) survey covering 184 arcmin(2) at 2 mm. Twelve of 13 detections above 5 sigma are attributed to emission from galaxies, 11 of which are dominated by cold dust emission. These sources have a median redshift of < Z(2) (mm)> = 3.6(-0.3)(+0.4) primarily based on optical/near-infrared photometric redshifts with some spectroscopic redshifts, with 77% +/- 11% of sources at z > 3 and 38% +/- 12% of sources at z > 4. This implies that 2 mm selection is an efficient method for identifying the highest-redshift dusty star-forming galaxies (DSFGs). Lower-redshift DSFGs (z < 3) are far more numerous than those at z > 3 yet are likely to drop out at 2 mm. MORA shows that DSFGs with star formation rates in excess of 300 M-circle dot yr(-1) and a relative rarity of similar to 10(-5) Mpc(-3) contribute similar to 30% to the integrated star formation rate density at 3 < z < 6. The volume density of 2 mm selected DSFGs is consistent with predictions from some cosmological simulations and is similar to the volume density of their hypothesized descendants: massive, quiescent galaxies at z > 2. Analysis of MORA sources' spectral energy distributions hint at steeper empirically measured dust emissivity indices than reported in typical literature studies, with = 2.2(-0.4)(+0.5). The MORA survey represents an important step in taking census of obscured star formation in the universe's first few billion years, but larger area 2 mm surveys are needed to more fully characterize this rare population and push to the detection of the universe's first dusty galaxies.