Does core losses in a transformers depend on voltage?

The most contributing factor to core losses in Transformers is the material on which they are wound. Transformers wound on iron cores are roughly 75% efficient but they can transfer large amounts of power at low frequency. Transformers wound on ferrite are typically better then 90% efficient but can't be used to transfer the same amount of power unless the frequency is increased. Switch mode power supplies do this.

After that, the voltage, impedance and current are all related. If you increase the current (by increasing the voltage) there are more losses because the magnetic field strength is not directly proportional to the current. The impedance remains the same for the same number of turns. Transformers are wound to the best compromise between efficiency and transfer capability. If you try to increase the voltage too much, the core will saturate and behave like a straight piece of wire.