We present four epochs of high-resolution IR spectroscopy of the peculiar X-ray binary Cygnus X-3. The observations cover quiescent, small flaring and outburst states of the system as defined by radio and X-ray monitoring. The underlying IR spectrum of the source, as observed during radio and X-ray quiescence and small flaring states is one of broad, weak He II and N V emission. Spectral variability in this state is dominated by modulation at the 4.8 hr orbital period of the system. H-band spectra confirm the significant hydrogen depletion of the mass donor. In outburst, the infrared spectrum is dramatically different, with the appearance of very strong twin-peaked He I emission displaying both day-to-day variability and V (iolet) / R(ed) variations with orbital phase. We argue that the most likely explanation appears to be an enhanced stellar wind from the companion. Thus the X-ray and radio outbursts in this system are likely to originate in mass-transfer, and not disc instabilities. We suggest that the wind in Cyg X-3 is significantly flattened in the plane of the binary orbit. This may explain the observed twin-peaked He I features as well as reconcile the large infrared luminosity with the large optical depth to X-rays if Cyg X-3 is embedded in a spherically symmetric wind.