Glacier surface facies are valuable indicators of changes experienced by a glacial system. The interplay of accumulation and ablation facies, followed by intermixing with dust and debris, as well as the local climate, all induce observable and mappable changes on the supraglacial terrain. In the absence or lag of continuous field monitoring, remote sensing observations become vital for maintaining a constant supply of measurable data. However, remote satellite observations suffer from atmospheric effects, resolution disparity, and use of a multitude of mapping methods. Efficient image-processing routines are, hence, necessary to prepare and test the derivable data for mapping applications. The existing literature provides an application-centric view for selection of image processing schemes. This can create confusion, as it is not clear which method of atmospheric correction would be ideal for retrieving facies spectral reflectance, nor are the effects of pansharpening examined on facies. Moreover, with a variety of supervised classifiers and target detection methods now available, it is prudent to test the impact of variations in processing schemes on the resultant thematic classifications. In this context, the current study set its experimental goals. Using very-high-resolution (VHR) WorldView-2 data, we aimed to test the effects of three common atmospheric correction methods, viz. Dark Object Subtraction (DOS), Quick Atmospheric Correction (QUAC), and Fast Line-of-Sight Atmospheric Analysis of Hypercubes (FLAASH); and two pansharpening methods, viz. Gram–Schmidt (GS) and Hyperspherical Color Sharpening (HCS), on thematic classification of facies using 12 supervised classifiers. The conventional classifiers included: Mahalanobis Distance (MHD), Maximum Likelihood (MXL), Minimum Distance to Mean (MD), Spectral Angle Mapper (SAM), and Winner Takes All (WTA). The advanced/target detection classifiers consisted of: Adaptive Coherence Estimator (ACE), Constrained Energy Minimization (CEM), Matched Filtering (MF), Mixture-Tuned Matched Filtering (MTMF), Mixture-Tuned Target-Constrained Interference-Minimized Filter (MTTCIMF), Orthogonal Space Projection (OSP), and Target-Constrained Interference-Minimized Filter (TCIMF). This experiment was performed on glaciers at two test sites, Ny-Ålesund, Svalbard, Norway; and Chandra–Bhaga basin, Himalaya, India. The overall performance suggested that the FLAASH correction delivered realistic reflectance spectra, while DOS delivered the least realistic. Spectra derived from HCS sharpened subsets seemed to match the average reflectance trends, whereas GS reduced the overall reflectance. WTA classification of the DOS subsets achieved the highest overall accuracy (0.81). MTTCIMF classification of the FLAASH subsets yielded the lowest overall accuracy of 0.01. However, FLAASH consistently provided better performance (less variable and generally accurate) than DOS and QUAC, making it the more reliable and hence recommended algorithm. While HCS-pansharpened classification achieved a lower error rate (0.71) in comparison to GS pansharpening (0.76), neither significantly improved accuracy nor efficiency. The Ny-Ålesund glacier facies were best classified using MXL (error rate = 0.49) and WTA classifiers (error rate = 0.53), whereas the Himalayan glacier facies were best classified using MD (error rate = 0.61) and WTA (error rate = 0.45). The final comparative analysis of classifiers based on the total error rate across all atmospheric corrections and pansharpening methods yielded the following reliability order: MXL > WTA > MHD > ACE > MD > CEM = MF > SAM > MTMF = TCIMF > OSP > MTTCIMF. The findings of the current study suggested that for VHR visible near-infrared (VNIR) mapping of facies, FLAASH was the best atmospheric correction, while MXL may deliver reliable thematic classification. Moreover, an extensive account of the varying exertions of each processing scheme is discussed, and could be transferable when compared against other VHR VNIR mapping methods.