Very few studies have been conducted to infer genotype × environment interaction (G×E) based in genomic prediction models using SNP markers. Therefore, our main objective was to compare a conventional genomic-based single-step model (HBLUP) with its reaction norm model extension (genomic 1-step linear reaction norm model [HLRNM]) to provide EBV for tick resistance as well as to compare predictive performance of these models with counterpart models that ignore SNP marker information, that is, a linear animal model (ABLUP) and its reaction norm extension (1-step linear reaction norm model [ALRNM]). Phenotypes included 10,673 tick counts on 4,363 Hereford and Braford animals, of which 3,591 were genotyped. Using the deviance information criterion for model choice, ABLUP and HBLUP seemed to be poorer fitting in comparison with their respective genomic model extensions. The HLRNM estimated lower average and reaction norm genetic variability compared with the ALRNM, whereas ABLUP and HBLUP seemed to be poorer fitting in comparison with their respective genomic reaction norm model extensions. Heritability and repeatability estimates varied along the environmental gradient (EG) and the genetic correlations were remarkably low between high and low EG, indicating the presence of G×E for tick resistance in these populations. Based on 5-fold -means partitioning, mean cross-validation estimates with their respective SE of predictive accuracy were 0.66 (SE 0.02), 0.67 (SE 0.02), 0.67 (SE 0.02), and 0.66 (SE 0.02) for ABLUP, HBLUP, HLRNM, and ALRNM, respectively. For 5-fold random partitioning, HLRNM (0.71 ± 0.01) was statistically different from ABLUP (0.67 ± 0.01). However, no statistical significance was reported when considering HBLUP (0.70 ± 0.01) and ALRNM (0.70 ± 0.01). Our results suggest that SNP marker information does not lead to higher prediction accuracies in reaction norm models. Furthermore, these accuracies decreased as the tick infestation level increased and as the relationship between animals in training and validation data sets decreased.