On a model train transformer, the outlet cord goes to a small winding, and the other is bigger and goes to circuit board. Which is primary?

The primary is the winding connected to a power source, the outlet.

You know which winding connects where so what does it matter what they are called? Actually, in a transformer, which winding is called primary serves little purpose except as a conceptual aid. Transformers can and often are used "backwards". There is a voltage ratio set by the turns ratio and it matters little which is the source and which is the load.

Outlet cord?

What is that?

A train transformer primary connects to the house power (mains) and the secondary goes to rectifiers and other things and is connected to the train track.

Maybe what you call the outlet cord, I am calling the inlet cord (input cord).

Confusion of words here. The "outlet cord" presumably is the one that connects to the wall outlet (socket) but as far as the transformer is concerned it brings electricity into the system, so it is really an input cord. The winding to which it is connected you describe as small. In fact although the wire has a small diameter there are many more turns on this side, which is the primary. The secondary winding uses many fewer turns of much thicker wire. That is the side which goes to the circuit board.

The AC cord is connected to the primary winding.

It is customary to connect the source Voltage across the primary of a transformer regardless of whether it's a Voltage step up or step down transformer. In this application you have no choice. The outlet (source) Voltage must be connected across the small winding. Therefore what you call the small winding is the primary.

The winding with the largest diameter wire is the winding that can safely handle the most current. If by bigger you meant larger diameter wire then that would be an indication that this is a Voltage step down transformer since (Vp)*(Ip) = (Vs)*(Is).

THE SMALL WINDING HAS THIN WIRE IS THE PRIMARY WINDING.

Another way to understand the answer is to realize that you want to reduce the voltage going to the train motor so the side of the transformer with the smaller windings will be supplying the motor and the other side will be connected to the power outlet or high voltage side.

The voltage is reduced so it will be safe for the user of the model train which is commonly a child.