You need similar tires on all four wheels. If you put snow tires just on the front, the rear will try to pass you if you try to stop in a turn. The VSC can correct somewhat, but it can't give you any more traction. If you put them just on the rear, you won't have as much traction for starting, stopping, or turning, which are done mainly by the front tires. Chains are OK on just two wheels according to most owner's manuals, but you can't drive over 25mph with them, and they are a pain to put on. You might carry some just in case, but don't plan on using them often. There are low profile chains/cables/devices that will fit any vehicle. I don't think the prius is that tight of a fit. Check out
http://www.scc-chain.com/ or Thule.
Studless snow tires are as good or better than studded tires for everything (packed snow, slush, wet, dry) except slick ice. I'd go with studless snow tires for a quieter ride and to save the roads. Studs are legal in Colorado (year round, apparently?), but they destroy the roads. We have to pay for that in taxes, fees, surcharges, tolls, etc, so might as well save the roads and keep costs down.
A prius will be fine in the snow with god tires. Last year there was a huge storm that caused chaos on I70. There were all sorts of cars abandoned on the road up to the eisenhower tunnel, and only a few cars were able to make it past all the accidents. But as we were driving a tiny hatchback with chains on the front wheels passed everyone! Personally I saw no need to pass anyone or go faster, but they didn't seem to have any trouble.
You probably don't want to turn VSC off. It will keep you from accelerating quickly sometimes, but it does that to keep you from spinning the wheels, which is usually counter-productive. It is good because it can apply the brakes to individual wheels to keep you going in the direction you are pointing the steering wheel (up to a limit. It will beep if it can't correct enough). There's no way you can do that with one brake pedal, and there's no way you can react as quickly as it can.
If you think you want to get a second set of rims, figure out what you will do about TPMS sensors. My vehicle will only recognize one set of sensors, so if I had another set of rims with another set of sensors I would have to have it reprogramed at the dealer for $$$. Sensors are not cheap either. You could run with no sensors in the winter, but some tire shops refuse to defeat the system if your car originally came with it. Plus it's nice to have the system to alert you if you get a flat, or if you are too lazy to check the pressure yourself. Or you can just have the tires swapped over to your rims, which should cost around $50 each time.