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_ u 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.
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