This article studies the snow plow routing problem, which is a modified version of the min–max problem with k-vehicles for arc routing on a mixed graph with hierarchy. Each arc or edge is given a priority and instead of minimizing the overall finishing time, we minimize the latest finishing time for each priority class. We consider turn restrictions, route balancing, and variable vehicle speeds in a real large-scale network. To solve the problem, we present a graph transformation from a directed rural postman problem with turn penalties to an asymmetric traveling salesman problem. We then make the following modifications to the metaheuristics to better handle the constraints: development of new neighborhood operators, several applications of the same destruction operators before repair of the solution, and a dynamic arc-grouping procedure when links are removed or inserted. We tested our methodology on three real networks with 1,626 to 2,146 street segments and 613 to 723 intersections. The results show that our approach can improve the solution, and the grouping procedure is helpful. The results also show that some operators perform better than others; the network topology seems to explain these variations. Finally, we validated our methodology by comparing to some routes planned in the past and to some routes obtained from a commercial solver.