Anosmia was identified as a hallmark of COVID-19 early in the pandemic, however, with the emergence of variants of concern, the clinical profile induced by SARS-CoV-2 infection has changed, with anosmia being less frequent. Several studies have focused on the neuropathogenesis of the original SARS-CoV-2, but little is known about the neuropathological potential of the variants. Here, we assessed the clinical, olfactory and inflammatory conditions of golden hamsters infected with the original SARS-CoV-2, its ORF7-deleted mutant, and three variants: Gamma, Delta and Omicron/BA.1. We show that infected animals developed a variant-dependent clinical disease, and that the ORF7 of SARS-CoV-2 contribute to causing olfactory disturbances. Conversely, all SARS-CoV-2 variants were found to be neuroinvasive, regardless of the clinical presentation they induce. With newly-generated nanoluciferase-expressing SARS-CoV-2, we validated the olfactory pathway as a main entry point towards the brain, confirming that neuroinvasion and anosmia are independent phenomena upon SARS-CoV-2 infection.