Well, if termina is in the lost woods, there is no proof to support Termina being a alternate dimmension.
Except it isn't in the Lost Woods. You fall down a hole, go through all these wonky portals and twisted passages then you end up in the middle of a town in a clock tower despite having fallen so far down. Also the manual describes it as a parallel world. Link fell through a portal to that world, the portal is in the woods but Termina isn't.