Do you think the rangers of the Night’s Watch ever have to help with builder and steward duties, especially preparing for/getting through winter?

Almost certainly. Given that they’re out in the wild, I imagine at the very least part of their work is hunting game for food, gathering wood for fires, etc. 

And when it’s too cold/snowy to go out and range, I imagine they’re retasked to do boring but important work at the Wall: helping to maintain/repair the Wall (after all, they have to patrol the thing), maintaining and repairing arms and armor (they have the experience to know how important it is to have your fighting gear in good nick), and so on.