I think that's sensible.
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I'm also doing a bit of google-fu here: our (Ant)arctic temps average a solid -44°F, firmly in the "extreme cold" category. That's a polar region on an otherwise ideally-habitable planet.
Something like Europa on the other hand, a more fitting analogue here, is more than -250⁰F at its equator. Definitely some "incredible cold."
In the ideal case then, we're looking at minor cold damage every hour ― more likely, minor cold damage every 10 min.
I think we'll have to stick this one close to the ship, what with exhaustion possible on top of the damage. This will be tricky seeing as there's not a good place to land close by. I'd also recommend we err on the side of being ready to flee. Combat is going to be extra dangerous here.