Snow golems are hardcoded to catch on fire in biomes where the temperature is above a certain value. The relevant snippet from MCP is:

    if (this.worldObj.getBiomeGenForCoords(i, j).getFloatTemperature() > 1.0F)
    {
        this.attackEntityFrom(DamageSource.onFire, 1.0F);
    }

This finds the biome of the snow golem's current location, checks if the biome's temperature setting is higher than 1.0, then sets the golem on fire if so.

Therefore, a costly way you can make a snow golem survive in the Nether is by bathing it in a constant supply of Fire Resistance potions. This will keep it from taking damage from the fire effect that being in warm biomes causes it.