<jats:p><jats:italic>Context.</jats:italic> The water snow line divides dry and icy solid material in protoplanetary disks. It has been thought to significantly affect planet formation at all stages. If dry particles break up more easily than icy ones, then the snow line causes a traffic jam because small grains drift inward at lower speeds than larger pebbles.</jats:p> <jats:p><jats:italic>Aims.</jats:italic> We aim to evaluate the effect of high dust concentrations around the snow line onto the gas dynamics.</jats:p> <jats:p><jats:italic>Methods.</jats:italic> Using numerical simulations, we modeled the global radial evolution of an axisymmetric protoplanetary disk. Our model includes particle growth, the evaporation and recondensation of water, and the back-reaction of dust onto the gas. The model takes into account the vertical distribution of dust particles.</jats:p> <jats:p><jats:italic>Results.</jats:italic> We find that the dust back-reaction can stop and even reverse the net flux of gas outside the snow line, decreasing the gas accretion rate onto the star to under 50% of its initial value. At the same time, the dust accumulates at the snow line, reaching dust-to-gas ratios of <jats:italic>ɛ</jats:italic> ≳ 0.8, and it delivers large amounts of water vapor towards the inner disk as the icy particles cross the snowline. However, the accumulation of dust at the snow line and the decrease in the gas accretion rate only take place if the global dust-to-gas ratio is high (<jats:italic>ε</jats:italic><jats:sub>0</jats:sub> ≳ 0.03), the viscous turbulence is low (<jats:italic>α</jats:italic><jats:sub><jats:italic>ν</jats:italic></jats:sub> ≲ 10<jats:sup>−3</jats:sup>), the disk is large enough (<jats:italic>r</jats:italic><jats:sub>c</jats:sub> ≳ 100 au), and only during the early phases of the disk evolution (<jats:italic>t</jats:italic> ≲ 1 Myr). Otherwise the dust back-reaction fails to perturb the gas motion.</jats:p>