Surely the blue ice effect will only be an issue in certain lighting conditions.
An open ice plane would only reflect a blue sky directly upwards, A cliff would only reflect blue if the light was such that the sky colour would bounce more than the hue of direct sunlight.
Inside a cave I doubt if you would get any blue reflection at all.
This is a common misconception. Water and ice don't look blue because of the sky, they look blue because they ARE blue.
H2O absorbs red light, giving water its blue look.
It has nothing to do with the reflection of a blue sky (well, that probably helps as well).