The European Space Agency Sentinel-2 satellites provide multispectral images with pixel sizes down to 10 m. This high resolution allows for fast and frequent detection, classification and discrimination of various objects in the sea, which is relevant in general and specifically for the vast Arctic environment. We analyze several sets of multispectral image data from Denmark and Greenland fall and winter, and describe a supervised search and classification algorithm based on physical parameters that successfully finds and classifies all objects in the sea with reflectance above a threshold. It discriminates between objects like ships, islands, wakes, and icebergs, ice floes, and clouds with accuracy better than 90%. Pan-sharpening the infrared bands leads to classification and discrimination of ice floes and clouds better than 95%. For complex images with abundant ice floes or clouds, however, the false alarm rate dominates for small non-sailing boats.