“Positioning yourself” in a ring presumably means being in orbit. In which case you’d be in the same orbit as the ring particles, or very close to it, and so relative velocities would be small.
But what if you remained stationary, while the rings spin, hurling snowballs at you?
Or if you try to fight that hypothetical, lets rephrase it thus:
Suppose you were standing in a field on Earth, with machines throwing snowballs in your general direction. The snowballs:
- are at the same temperature, density, and hardness as the particles in Saturn’s rings.
- are propelled at the same velocity as Saturn’s fastest ring spins.
- have a range of sizes typical of the particles in Saturn’s rings
- have the same distance apart as typical of the particles of Saturn’s rings
Given this scenario, how much trouble are you in?
- Life ending in 0.001 seconds?
- Unlikely to be hit at all?
- Might be hit, but with a soft bit of snow that won’t hurt you?
You’ll be smeared across the landscape in even less time than that.
I can’t answer that question, but I’ll note that the rings are surprisingly thin, mostly only about 10 meters thick (yes meters). So if you’re in the ring plane, you are likely to be hit by any particle orbiting at the same distance from Saturn as you are, since all the ring material is confined to a plane not much bigger than you are.
The rings are moving at orbital velocity. The outer ring is at 16.5 km/s, and the inner at 22.5 km/s.
A nickel traveling at 22.5 km/s would have about the kinetic energy of a stick of dynamite.
Just to put some numbers on this:
- The mass density of the inner edge of the B ring, according to these figures, is within an order of magnitude of \rho \approx 50 kg/m3.
- The speed of the particles at the inner edge of the B ring is about v \approx 20 km/s.
- The kinetic energy flux of a mass density flowing at a speed v is \frac12 \rho v ^3. Combining these numbers, we get about… 2 \times 10^{14} watts per square meter. Since an average human body has an cross-sectional area of about one square meter, that means that your body is going to have to continuously absorb or deflect about 200 terawatts of energy.
I don’t think I could do it, personally, but maybe you work out more than I do.
To finish the pile-on, the entire USA’s electrical generating capacity is about 1.2 terawatts. So figure energy equal to ~160 complete USAs’-worth of electricity.
As for this one: one could perhaps imagine that the density is so low that you’re unlikely to be actually hit (like traveling through the asteroid belt or Oort cloud).
But that’s not true here. The average density of the rings is about 10 kg/m^3, according to this post:
If the rings are moving at 22.5 km/s, and you have a frontal surface area of about 1 m^2, then there are about 225 tons of “stuff” passing through you per second. And this mass is not concentrated into large objects. It’s anywhere from dust to kilogram-scale chunks. You’d be hit almost instantly with something and turned to a fine mist.
Shoulda refreshed. 
I think both calculations are useful 
. Tons of mass per second vs. “USAs worth of electricity” are both fairly intuitive.
“A few of you will be forced through a fine mesh screen for your planet.”
It would be cool if we finally got imagery of the objects in the rings and it all turned out to be skeletons and frozen chunks of flesh.
And a bit terrifying
As long as it’s composed mostly of centimeter-sized chunks of annoying Pekinese I’m all for it.
Somehow it wouldn’t surprise me to learn that Florida is the Pekingese capital of the US. Remarkably, there are no yippy dogs around where I live.
Naaah. The capital is NYC & environs. They migrate down here w their equally irritating humans semi-annually.