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 less than or similar to z less than or similar to 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 similar to 0.06-0.1 mag with 1.5 sigma-2.5 sigma 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 similar 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.