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I've read that NiMH and Lithium chemistries will only supply around half of their rated capacity when used at low temperatures (say around 0 degrees C).

Many sources also mention an increase in internal resistance and it is inferred that the two characteristics are related.

Now what if I'm working on a very low current application relative to the C rating of the battery? Say 0.01C. Do I still have to assume I will only get roughly half the mAh out of the battery? (My reasoning is that at low C discharge rates the internal resistance of the battery is less significant.)

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The reasoning about the internal resistance is correct. To illustrate it, I found this plot for different discharge rates at low temperatures.

enter image description here

Energizer L91 Lithium Battery Capacity and Temperature Curve. Source.

There is another discussion about temperature and discharge rate here.

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