We use high-resolution cosmological zoom simulations with ~200 pc resolution at z = 2 and various prescriptions for galactic outflows in order to explore the impact of winds on the morphological, dynamical, and structural properties of eight individual galaxies with halo masses ~ 10^11--2x10^12 Msun at z = 2. We present a detailed comparison to spatially and spectrally resolved H{alpha} and other observations of z ~ 2 galaxies. We find that simulations without winds produce massive, compact galaxies with low gas fractions, super-solar metallicities, high bulge fractions, and much of the star formation concentrated within the inner kpc. Strong winds are required to maintain high gas fractions, redistribute star-forming gas over larger scales, and increase the velocity dispersion of simulated galaxies, more in agreement with the large, extended, turbulent disks typical of high-redshift star-forming galaxies. Winds also suppress early star formation to produce high-redshift cosmic star formation efficiencies in better agreement with observations. Sizes, rotation velocities, and velocity dispersions all scale with stellar mass in accord with observations. Our simulations produce a diversity of morphological characteristics - among our three most massive galaxies, we find a quiescent grand-design spiral, a very compact star-forming galaxy, and a clumpy disk undergoing a minor merger; the clumps are evident in H{alpha} but not in the stars. Rotation curves are generally slowly rising, particularly when calculated using azimuthal velocities rather than enclosed mass. Our results are broadly resolution-converged. These results show that cosmological simulations including outflows can produce disk galaxies similar to those observed during the peak epoch of cosmic galaxy growth.
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