WISE has discovered an extraordinary population of hyper-luminous dusty galaxies which are faint in the two bluer passbands ($3.4\, μ$m and $4.6\, μ$m) but are bright in the two redder passbands of WISE ($12\, μ$m and $22\, μ$m). We report on initial follow-up observations of three of these hot, dust-obscured galaxies, or Hot DOGs, using the CARMA and SMA interferometer arrays at submm/mm wavelengths. We report continuum detections at $∼$ 1.3 mm of two sources (WISE J014946.17+235014.5 and WISE J223810.20+265319.7, hereafter W0149+2350 and W2238+2653, respectively), and upper limits to CO line emission at 3 mm in the observed frame for two sources (W0149+2350 and WISE J181417.29+341224.8, hereafter W1814+3412). The 1.3 mm continuum images have a resolution of 1-2 arcsec and are consistent with single point sources. We estimate the masses of cold dust are 2.0$\times 10^{8} M_{⊙}$ for W0149+2350 and 3.9$\times 10^{8} M_{⊙}$ for W2238+2653, comparable to cold dust masses of luminous quasars. We obtain 2$σ$ upper limits to the molecular gas masses traced by CO, which are 3.3$\times 10^{10} M_{⊙}$ and 2.3$\times 10^{10} M_{⊙}$ for W0149+2350 and W1814+3412, respectively. We also present high-resolution, near-IR imaging with WFC3 on the Hubble Space Telescope for W0149+2653 and with NIRC2 on Keck for W2238+2653. The near-IR images show morphological structure dominated by a single, centrally condensed source with effective radius less than 4 kpc. No signs of gravitational lensing are evident. ; Comment: 13 pages, 3 figures. ApJ in press