We present IRTF/SpeX and NEOWISE observations of the dynamically new comet C/2013 US$_{10}$ (Catalina), hereafter US10, from 5.8 au inbound, to near perihelion at 1.3 au, and back to 5.0 au outbound. We detect water ice in the coma of US10, assess and monitor the physical properties of the ice as insolation varies with heliocentric distance, and investigate the relationship between water ice and CO$_{2}$. This set of measurements is unique in orbital coverage and can be used to infer the physical evolution of the ice and, potentially, the nucleus composition. We report (1) nearly identical near-infrared spectroscopic measurements of the coma at $-$5.8 au, $-$5.0 au, +3.9 au (where $<$0 au indicates pre-perihelion epochs), all presenting evidence of water-ice grains, (2) a dust-dominated coma at 1.3 au and 2.3 au and, (3) an increasing CO$_{2}$/$Afrho$ ratio from $-$4.9 au to 1.8 au. We propose that sublimation of the hyper-volatile CO$_{2}$ is responsible for dragging water-ice grains into the coma throughout the orbit. Once in the coma, the observability of the water-ice grains is controlled by the ice grain sublimation lifetime, which seems to require some small dust contaminant (i.e., non-pure ice grains). At |R$_{h}$|>=3.9 au, the ice grains are long-lived and may be unchanged since leaving the comet nucleus. We find the nucleus of comet US10 is made of, among other components, $sim$1-micron water-ice grains containing up to 1% refractory materials.
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