I think you're looking for Blizzard Island. To borrow from the IMDB summary for The Argon Quest, which was a TV movie cobbled together from the first few episodes:
Siblings Tracy and Wayne find a mysterious artifact that teleports them to Blizzard Island, a magical place full of strange creatures. They discover that the island is slowly dying, and the only way to save it is by finding and waking up the giant Argon. However, the evil witch Sidney won't have any of that...
They find the artifact in a chest in the attic, which comes from their father, a sailor lost at sea. One of the first puppets we encounter is a green puppet snake with a top hat in a forest.
First episode of Blizzard Island
Found with a search for 80s tv series puppets brother sister attic portal, which led to this discussion forum, where someone was looking for it. You can find more information on Terry Angus's site.