Yes, many of the Osmo games will work on the iPad Mini and iPad Air. For reference, here's a list of iPad models that Osmo is compatible with.
(Note: the Math Wizard games are not compatible with the Mini 1, but are compatible with the other Mini's).
Additionally, Osmo is not currently compatible with the iPad Air 4, which was just released on September 18, 2020. While we hope to be compatible with the iPad Air 4, it will take us some time to complete the assessment.
Need help getting started with your compatible iPad? Review setup instructions here.