Naturally he wishes to wander in.

This particular snake has a score to settle for being made to reveal that he likely intends on eventually accepting a marriage proposal, and he intends to make that settling both as painful and pleasurable a lesson as possible.

He slithers inside and direct to where sun is spilling in through the windows, finding a patch of floor to bask as if he were any ordinary snake. Come closer, foolish prince, there's nothing to fear here.