"Na" in the meaning of "on" or "at" is followed by the locative case. "Nohou" is the locative plural form of "noha."
Yep. I will just add that 'nohou' is a remnant dual form that is used with body parts :)
If "noha" is meant as a part of the body. 6. case (o) kom, čem "nohou" and also "nohách"
I'd like to ask what says, in this sentence, that it's on "our" feet and not just "on feet?
Czech does not like possessives the way English does. Be prepared to see many more sentences like this one.
We don't say 'on feet' in English. We say 'on our feet'. The exception is 'on foot' which means something rather different: on foot rather than by bicycle or by car.