The writing is grammatical, but not exactly natural for native speakers.
We can use combined with as it's used in the text you provided. We can also use along with to give the same meaning.
We can also use coupled with, but to couple means to join two things, or to refer to two things jointly. There are three things mentioned in the text, but we can conceptualize the idea as (A + B) + C.
A more standard way to give the idea expressed is:
Without a ground sheet or even an earth pad, the killing cold temperature and the cutting wind, combined with our clammy feet, made us feel like we wouldn't survive the night.
The commas I have added shift the meaning to suggest that all three things together made us worry.
Without the commas, it tends more to suggest that these factors acted to link themselves together, or that an external force or agent put them together. This distinction can be a subtle one, or an important one, depending on the context.
Along with stands apart from the other choices because it is more likely to suggest that we are referring to things collectively, and does not carry the possible connotation that the things were combined as an action.