Numerous landscape genomic studies have identified single-nucleotide polymorphisms (SNPs) and genes potentially involved in local adaptation. Rarely, it has been explicitly evaluated whether these environmental associations also hold true beyond the populations studied. We tested whether putatively adaptive SNPs in Arabidopsis halleri (Brassicaceae), characterized in a previous study investigating local adaptation to a highly heterogeneous environment, show the same environmental associations in an independent, geographically enlarged set of 18 populations. We analysed new SNP data of 444 plants with the same methodology (partial Mantel tests, PMTs) as in the original study and additionally with a latent factor mixed model (LFMM) approach. Of the 74 candidate SNPs, 41% (PMTs) and 51% (LFMM) were associated with environmental factors in the independent data set. However, only 5% (PMTs) and 15% (LFMM) of the associations showed the same environment–allele relationships as in the original study. In total, we found 11 genes (31%) containing the same association in the original and independent data set. These can be considered prime candidate genes for environmental adaptation at a broader geographical scale. Our results suggest that selection pressures in highly heterogeneous alpine environments vary locally and signatures of selection are likely to be population-specific. Thus, genotype-by-environment interactions underlying adaptation are more heterogeneous and complex than is often assumed, which might represent a problem when testing for adaptation at specific loci.