Should I ask my co-author before I upload an article (that he already told me is okay to publish) to arXiv? At our institute it is not common to upload a pre-print of your submission to arXiv. I got told by a friend that it is basically a no-brainer and there are virtually no downsides in doing so. I checked with the journal I want to publish in, they even allow submitting arXiv links, so I am safe from there.

Since nobody at my institute seems to upload their pre-prints, should I ask my advisor before doing so? He is also co-author of the paper.

My field of research is materials science (and to some extent more general physics).
Yes, you should check with any co-authors before publicly posting a preprint of work that is not yet published.

They may prefer that you not post it at this time (e.g. if they have a particular timeline in mind for when they want to publicly share the work, given other related things they are working on). Even if they have no reason to object, you should check with them as a courtesy.