1. A method, comprising: estimating a depth of frozen precipitation on at least a portion of a surface based on an accumulation rate of the frozen precipitation; receiving location data associated with a vehicle, wherein the vehicle is equipped to remove frozen precipitation from the surface; upon determining based on the received location data that the vehicle has passed over the portion of the surface, resetting the estimate of the current depth of the frozen precipitation on the portion of the surface; adjusting the estimate of the current depth to yield an adjusted depth of the frozen precipitation based on a received indicator of traffic density on the portion of the surface, the adjusted depth representing a compactness of the frozen precipitation; generating, by operation of one or more computer processors, a traveling cost for the portion of the surface based on the adjusted depth; and transmitting for display at least one of: (i) map data that associates the traveling cost to a particular geographic location and (ii) a planned route based on the traveling cost.