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Because this is linked to mythology, most of the references to them seem to be heavily invested in woo. However, it does seem that in this case, the snakes were real grass snakes (as the Wikipedia article notes, žaltys is literally 'grass snake' in Lithuanian) kept in the believer's homes.
Žaltys (pronounced zhal-TEES), a kind of grass snake, were kept in homes, usually near hearth fires, and were considered particularly sacred to the sun goddess. Saule was said to cry amber tears at the site of a dead žaltys. It was also believed that if a snake was given a fatal blow, it would not die until the sun had set. In 1604 a Jesuit missionary descrived the practice of keeping these house snakes, claiming the Balts had gone mad: "The people have reached such a stage of madness that they believe that deity exists in reptiles. Therefore they carefully safeguard them, lest someone injure the reptiles kept inside their homes. Superstitiously they believe that harm would come to them, should anyone show disrespect to these reptiles."
Drawing Down the Sun: Rekindle the Magick of the Solar Goddesses, Stephanie Woodfield