Embroidery design files (such as .art files for Bernina Artista machines) are saved basically in vector graphics format with additional instructions for the stitching machine.
As such it should be quite possible to export them and save as common SVG graphics (XML vectors). This can be usually done in embroidery programs with support of this function.
But, many graphics formats used art extension for their files in past years, so perhaps other art to svg conversion are also possible. In this case it would be best to use some dedicated vector graphics editor and hope that it supports your .art file.