Thank you for raising that good question. Apparently, cells in the nose are more prone to SARS-CoV-2 infection than cells in the mouth, according to this study (https://www.cell.com/cell/fulltext/S0092-8674(20)30675-9), which has been covered in several news outlets that may be easier to understand: e.g.,

https://abc11.com/unc-mask-study-below-nose-covid/6387870/.

That said, it's also true that they are natural hair filters in the nose. The study mentioned above is based on cell and tissue culture work, so it doesn't consider the hair filters and other natural or environmental factors. Not to mention that differences in nasal and oral microbiota between individuals might affect the risk of SARS-CoV-2 infection.

I think it would take unethical human trials to fully determine any differences in nose vs. mouth infection by and spread of SARS-CoV-2.