I'm working on a small cabin. All black wires are run directly to lights. The white wires are run to the switches then lights... so each switch has only white wires.
Would the circuit still work? Why or why not?
Aside from being a code violation of outrageous proportions, if this is 120VAC you would have the delightful condition that the light sockets were always hot/live - this can make changing a lightbulb into a shocking experience, and under the right conditions, also your last.
You may also get some interesting magnetic effects from the loop wiring.
Don't do this. The only level it "works" at is the Dr. Frankenstein's Laboratory level, and most people are not as tough as Igor. If it's actually something you found (or even, nay, especially, if it's something you are responsible for creating), rip it the heck out and do it right.
Maybe I'm answering too soon (hopefully you'll post a diagram and/or pictures). But offhand and assuming you're using 120V AC power, this doesn't sound so good. Yes, there's a fair chance that you could make it function, but probably not really in compliance with the rules. It sounds like at best you're switching on the neutrals, but it's hard to tell without more details.
I presume the cabin is supplied with 120V AC circuits? If this is actually 12V DC, you're going to be surprised at how big the wires need to be. You probably won't be happy with lighting over smaller than #10 wires because you get rapid voltage drop over short distances with low voltage, and smaller wires result in even more voltage drop. But with 12V low voltage circuits you also won't have the same code requirements as for 120/240V AC.
If you have single wires running independently to the light fixtures and the switches, you're not in code compliance (for residential AC service) even if the wires are in conduit (the wires for a circuit need to run together, so you can't run the "hot" and "neutral" along different routes). For a circuit to actually function, you need a supply conductor (the "hot," typically black) and a return conductor (the "neutral," typically white), and the electrical code requires a grounding conductor for anything new or anything you make substantial changes to.
If you were using standard 14/2 or 12/2 NM cable, you would have a black ("hot"), white ("neutral") and a bare grounding wire in each cable.
So you would have at least a black and a white conductor in each light fixture and in the switch box(es).
You'd have a supply cable feeding power into either the switch box or your light fixture(s). If power feeds into the light fixture, you'd have a switch loop to the switch box, which you would use 14/3 or 12/3 cable for (black, red and white plus a bare ground wire). That way you can provide a neutral in the switch box as required by current code and use the black and red for the switch loop for the supply side.