You're right, the N1 gage knows nothing of OAT - but the ENGINE does.
To reach a given EPR, the engine doesn't have to turn as fast on a cold day (high density = high mass flow at a given N1). This is the whole concept behind using N1 for power management (eg a GE or CFM engine); You can't know what N1 to set until you know OAT (and also pressure altitude...)