Is it normal for the cooling fans to come on right after starting the car? Even when the car is cool or cold, the fans come right on.

I believe the Legacy (2003) has a transmission cooler along with the regular cooling system? I have never heard a car use the cooling fans as much as this car does.

Check the coolant temp sensor or fan relays. Most probably Coolant temp sensor($25).

Post result back please. I am interested.