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 if so deals damage to the golem as if it were on fire.

Taken from the declarations in `BiomeGenBase`, the temperature of the Nether is a scorching `2.0`. The other vanilla biomes that have a temperature >1.0 are Desert (`2.0`), DesertHills (`2.0`), Jungle (`1.2`), and JungleHills (`1.2`).

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.