We present new infrared observations of the exotic X-ray binary system Cygnus X-3, including high-time-resolution simultaneous H- and K-band photometry over ~1.5 orbital periods and 1-5mum photometry during both periods of apparent infrared quiescence and flaring activity. The simultaneous H- and K-band observations reveal the 4.8-h orbital modulation of the source, superimposed upon which are a number of extremely rapid flare events. We find rise times for these events of <=15 s, and find that the source becomes redder in (H-K) during the flares. This latter effect is confirmed by 1-5 μm photometry during a period of prolonged quasi-stable flaring. We model this reddening in colour during flaring in terms of optically thin free-free emission from a hot dense plasma, possibly associated with a thermal gas in the high-velocity radio jets revealed by radio VLBI. Size, luminosity and lack of self-absorption considerations allow us to place strong constraints on possible values of N_e and T for this plasma, and we find that the dominant cooling mechanism is likely to be bremsstrahlung cooling. Dereddening of new 1-5mum data combined with 0.7-1.0mum results from the literature is consistent with an estimated infrared extinction to the source of 4.5<=A_J<=7.5 mag, and an infrared excess above a blackbody stellar continuum which is inherent to the source.