  Context. The water snowline divides dry and icy solid material in
protoplanetary disks, and has been thought to significantly affect planet
formation at all stages. If dry particles break up more easily than icy ones,
then the snowline causes a traffic jam, because small grains drift inward at
lower speeds than larger pebbles. Aims. We aim to evaluate the effect of high
dust concentrations around the snowline onto the gas dynamics. Methods. Using
numerical simulations, we model the global radial evolution of an axisymmetric
protoplanetary disk. Our model includes particle growth, evaporation and
recondensation of water, and the back-reaction of dust onto the gas, taking
into account the vertical distribution of dust particles. Results. We find that
the dust back-reaction can stop and even reverse the net flux of gas outside
the snowline, decreasing the gas accretion rate onto the star to under $50\%$
of its initial value. At the same time the dust accumulates at the snowline,
reaching dust-to-gas ratios of $\epsilon \gtrsim 0.8$, and delivers large
amounts of water vapor towards the inner disk, as the icy particles cross the
snowline. However, the accumulation of dust at the snowline and the decrease in
the gas accretion rate only take place if the global dust-to-gas ratio is high
($\varepsilon_0 \gtrsim 0.03$), if the viscous turbulence is low ($\alpha_\nu
\lesssim 10^{-3} $), if the disk is large enough ($r_c \gtrsim 100\,
\textrm{au}$), and only during the early phases of the disk evolution ($t
\lesssim 1\, \textrm{Myr}$). Otherwise the dust back-reaction fails to perturb
the gas motion.
