We report on observations of redshifted CO(1-0) line emission and observed-frame $rmsim$ 30GHz radio continuum emission from five ultra-luminous, mid-IR selected hot, Dust-Obscured Galaxies (Hot DOGs) at $zrmgtrsim$ 3 using the Karl G. Jansky Very Large Array. We detect CO(1-0) line emission in all five Hot DOGs, with one of them at high signal to noise. We analyse FIR-radio spectral energy distributions, including dust, free-free and synchrotron emission for the galaxies. We find that most of the 115 GHz rest-frame continuum is mostly due to synchrotron or free-free emission, with only a potentially small contribution from thermal emission. We see a deficit in the rest-frame 115 GHz continuum emission compared to dusty star-forming galaxies (DSFGs) and sub-millimetre galaxies (SMGs) at high redshift, suggesting that Hot DOGs do not have similar cold gas reserves compared with star-forming galaxies. One target, W2305-0039, is detected in the FIRST 1.4 GHz survey, and is likely to possess compact radio jets. We compare to the FIR-radio correlation, and find that at least half of the Hot DOGs in our sample are radio-quiet with respect to normal galaxies. These findings suggest that Hot DOGs have comparably less cold molecular gas than star-forming galaxies at lower, $zrmsim$ 2 redshifts, and are dominated by powerful, yet radio-quiet AGN.
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