As a major real-world problem, snow plowing has been studied extensively. However, most studies focus on deterministic settings with little urgency yet enough time to plan. In contrast, we assume a severe snowstorm with little known data and little time to plan. We introduce a novel time-dependent multi-visit dynamic safe street snow plowing problem and formulate it on a rolling-horizon-basis. To solve this problem, we develop an adaptive large neighborhood search as the underlying method and validate its efficacy on team orienteering arc routing problem benchmark instances. We create real-world-based instances for the city of Vienna and examine the effect of (i) different snowstorm movements, (ii) having perfect information, and (iii) different information-updating intervals and look-aheads for the rolling horizon method. Our findings show that different snowstorm movements have no significant effect on the choice of rolling horizon settings. They also indicate that (i) larger updating intervals are beneficial, if prediction errors are low, and (ii) larger look-aheads are better suited for larger updating intervals and vice versa. However, we observe that less look-ahead is needed when prediction errors are low.