  SNe driven winds are widely thought to be very influential in the
high-redshift Universe, shaping the properties of the circum-galactic medium,
enriching the IGM with metals and driving the evolution of low-mass galaxies.
However, it is not yet fully understood how SNe driven winds interact with
their surroundings in a cosmological context, nor is it clear whether they are
able to significantly impact the evolution of low-mass galaxies from which they
originate by altering the amount of cold material these accrete from the cosmic
web. We implement a standard Taylor-Sedov type solution, widely used in the
community to depict the combined action of many SN explosions, in a
cosmological resimulation of a low mass galaxy at z =9 from the 'Nut' suite.
However, in contrast with previous work, we achieve a resolution high enough to
capture individual SN remnants in the Taylor-Sedov phase, for which the
solution provides an accurate description of the expansion. We report the
development of a high-velocity, far-reaching galactic wind produced by the
combined action of SNe in the main galaxy and its satellites, which are located
in the same or a neighbouring dark matter halo. Despite this, we find that (i)
this wind carries out very little mass (the measured outflow is of the order of
a tenth of the inflow/star formation rate) and (ii) the cold gas inflow rate
remains essentially unchanged from the run without SNe feedback. Moreover,
there are epochs during which star formation is enhanced in the feedback run
relative to its radiative cooling only counterpart. We attribute this
'positive' feedback to the metal enrichment that is present only in the former.
We conclude that at very high redshift, efficient SNe feedback can drive
large-scale galactic winds but does not prevent massive cold gas inflow from
fuelling galaxies, resulting in long-lived episodes of intense star
formation.(abridged)
