We present measurements of the CO luminosity functions (LFs) and the evolution of the cosmic molecular gas density out to z ∼ 6 based on an 8.5 arcmin 2 spectral scan survey at 3 mm of the iconic Hubble Deep Field North (HDF-N) observed with the NOrthern Extended Millimeter Array (NOEMA). We use matched filtering to search for line emission from galaxies and determine their redshift probability distributions exploiting the extensive multiwavelength data for the HDF-N. We identify the seven highest-fidelity sources as CO emitters at 1 < z < 6, including the well-known submillimeter galaxy HDF 850.1 at z = 5.18. Four high-fidelity 3 mm continuum sources are found to be radio galaxies at z 1, plus HDF 850.1. We constrain the CO LFs in the HDF-N out to z ∼ 6, including a first measurement of the CO(5-4) LF at 〈z〉 = 5.0. The relatively large area and depth of the NOEMA HDF-N survey extends the existing LFs at 1 < z < 4 above the knee, yielding a somewhat lower density by 0.15-0.4 dex at the overlap region for the CO(2-1) and CO(3-2) transitions, attributed to cosmic variance. We perform a joint analysis of the CO LFs in the HDF-N and Hubble Ultra Deep Field from ASPECS, finding that they can be well described by a single Schechter function. The evolution of the cosmic molecular gas density from a joint analysis is in good agreement with earlier determinations. This implies that the impact of cosmic field-to-field variance on the measurements is consistent with previous estimates, adding to the challenges for simulations that model galaxies from first principles.