After more than 26 years in quiescence, the black hole transient V404 Cyg went into a luminous outburst in 2015 June, and additional activity was detected in late December of the same year. Here, we present an optical spectroscopic follow-up of the December mini-outburst, together with X-ray, optical and radio monitoring that spanned more than a month. Strong flares with gradually increasing intensity are detected in the three spectral ranges during the ∼10 d following the Swift trigger. Our optical spectra reveal the presence of a fast outflowing wind, as implied by the detection of a P-Cyg profile (He I-5876 Å) with a terminal velocity of ∼2500 km s-1 . Nebular-like spectra - with an Hα equivalent width of ∼500 Å - are also observed. All these features are similar to those seen during the main 2015 June outburst. Thus, the fast optical wind simultaneous with the radio jet is most likely present in every V404 Cyg outburst. Finally, we report on the detection of a strong radio flare in late 2016 January, when X-ray and optical monitoring had stopped due to Sun constraints.