We detect ionized gas characteristics indicative of winds in three disk-dominated galaxies that are members of a super-group at z = 0.37 that will merge to form a Coma-mass cluster. All three galaxies are IR luminous (L IR > 4 × 1010 L sun, SFR > 8 M sun yr-1) and lie outside the X-ray cores of the galaxy groups. We find that the most IR-luminous galaxy has strong blueshifted and redshifted emission lines with velocities of ~ ± 200 km s-1 and a third, blueshifted (~900 km s-1) component. This galaxy's line widths (Hβ, [O III]λ5007, [N II], Hα) correspond to velocities of 100-1000 km s-1. We detect extraplanar gas in two of the three galaxies with SFR >8 M sun yr-1 whose orientations are approximately edge-on and which have integral field unit (IFU) spaxels off the stellar disk. IFU maps reveal that the extraplanar gas extends to rh ~ 10 kpc [N II] and Hα line widths correspond to velocities of ~200-400 km s-1 in the disk and decrease to ~50-150 km s-1 above the disk. Multi-wavelength observations indicate that the emission is dominated by star formation. Including the most IR-luminous galaxy we find that 18% of supergroup members with SFR >8 M sun yr-1 show ionized gas characteristics indicative of outflows. This is a lower limit as showing that gas is outflowing in the remaining, moderately inclined, galaxies requires a non-trivial decoupling of contributions to the emission lines from rotational and turbulent motion. Ionized gas mass loss in these winds is ~0.1 M sun yr-1 for each galaxy, although the winds are likely to entrain significantly larger amounts of mass in neutral and molecular gases.