This research is related to the exploitation of multispectral imagery from an unmanned aerial vehicle (UAV) in the assessment of damage to rapeseed after winter. Such damage is one of a few cases for which reimbursement may be claimed in agricultural insurance. Since direct measurements are difficult in such a case, mainly because of large, unreachable areas, it is therefore important to be able to use remote sensing in the assessment of the plant surface affected by frost damage. In this experiment, UAV images were taken using a Sequoia multispectral camera that collected data in four spectral bands: green, red, red-edge, and near-infrared. Data were acquired from three altitudes above the ground, which resulted in different ground sampling distances. Within several tests, various vegetation indices, calculated based on four spectral bands, were used in the experiment (normalized difference vegetation index (NDVI), normalized difference vegetation index—red edge (NDVI_RE), optimized soil adjusted vegetation index (OSAVI), optimized soil adjusted vegetation index—red edge (OSAVI_RE), soil adjusted vegetation index (SAVI), soil adjusted vegetation index—red edge (SAVI_RE)). As a result, selected vegetation indices were provided to classify the areas which qualified for reimbursement due to frost damage. The negative influence of visible technical roads was proved and eliminated using OBIA (object-based image analysis) to select and remove roads from classified images selected for classification. Detection of damaged areas was performed using three different approaches, one object-based and two pixel-based. Different ground sampling distances and different vegetation indices were tested within the experiment, which demonstrated the possibility of using the modern low-altitude photogrammetry of a UAV platform with a multispectral sensor in applications related to agriculture. Within the tests performed, it was shown that detection using UAV-based multispectral data can be a successful alternative for direct measurements in a field to estimate the area of winterkill damage. The best results were achieved in the study of damage detection using OSAVI and NDVI and images with ground sampling distance (GSD) = 10 cm, with an overall classification accuracy of 95% and a F1-score value of 0.87. Other results of approaches with different flight settings and vegetation indices were also promising.