This paper addresses the issue of optimal day-ahead scheduling of a plug-in electric vehicles (PEVs) aggregator that participates in the electricity market and offers an out-of-market balancing service to the local renewable power penetrated distribution system in a snow-prone area. The proposed balancing service provides a reliable source of flexibility for the extra real-time energy demand of the distribution system operator (DSO) which originates from the difference between its day-ahead bids and the actual demand. The problem is investigated on a snowy day when the DSO's day-ahead decisions encounter more uncertainty due to the considerable effect of snow loss on the DSO's photovoltaic plant performance. The aggregator's scheduling is formulated as two-stage stochastic programming which minimizes the PEVs’ charging cost. Monte Carlo simulation and K-means clustering are implemented to generate scenarios of driving patterns and real-time energy market prices, respectively. Offering the balancing service requires day-ahead predictions of the photovoltaic power and the grid load demand which are modeled using long short-term memory networks. The problem is formulated as mixed-integer linear programming. The results show that the proposed scheduling approach reduces the PEVs’ charging cost by 53% and guarantees the grid normal operation. Moreover, the balancing service can reduce the expected PEVs’ charging cost and the DSO's real-time cost by 12% and 14%, respectively.