Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012 to 2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SNe Ia (0.2 ≤ z ≤ 0.6) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-z HST data with 42 SNe Ia at z < 0.1 observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical photometry) to pursue a unique avenue to constrain the dark energy equation-of-state parameter, w. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size ∼0.06-0.1 mag with 1.5σ-2.5σ significance depending on the method and step location used. Combining our NIR sample with cosmic microwave background constraints, we find 1 + w = -0.17 ± 0.12 (statistical + systematic errors). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measure H 0 = 75.9 ± 2.2 km s-1 Mpc-1 from stars with geometric distance calibration in the hosts of eight SNe Ia observed in the NIR versus H 0 = 71.2 ± 3.8 km s-1 Mpc-1 using an inverse distance ladder approach tied to Planck. Using optical data, we find 1 + w = -0.10 ± 0.09, and with optical and NIR data combined, we find 1 + w = -0.06 ± 0.07; these shifts of up to ∼0.11 in w could point to inconsistency in the optical versus NIR SN models. There will be many opportunities to improve this NIR measurement and better understand systematic uncertainties through larger low-z samples, new light-curve models, calibration improvements, and eventually by building high-z samples from the Roman Space Telescope.