Was Satan an Actual Serpent in the Garden?

The Bible portrays Satan and his demons as spirits. So then, how can both Satan and a real serpent be the culprit? From other passages we find an important principle. Satan and demons can enter into people and animals and influence them.

Then Satan entered Judas, called Iscariot, one of the twelve. And Judas went to the chief priest and the officers of the temple guard and discussed with them how he might betray Jesus.

Luke 22:3-4

So we can understand the serpent was indeed a real serpent, but one which has been entered into and taken over by Satan.