For reference, here is an image of Saturn, where you can clearly see the shadow cast by the rings on the planet's surface:
As you can see, the shadow is quite dark. It's also quite wide. If you were standing in the middle of that shadow, at that time of year, the sun would be entirely covered by the rings for many miles in every direction, and you would only see whatever glimmers of sunlight were able to penetrate the icy mass of the rings. The sun would appear as though shining through a cloud - how heavy a cloud is up to you, as it depends on how thick the rings are. With the shadow as wide as it is during the time of year depicted, there would be no glow around the horizon as is described during a total solar eclipse on Earth, because everything for many, many miles around falls under the same shadow. The rings themselves, though casting the shadow, are backlit by the sun and so appear as the brightest thing in the sky, stretching from horizon to horizon in a glowing arc.
Another important thing that you'll notice in the picture is that the ring shadows do not run perpendicular to the planet's axis of spin. This means that, during the course of a day, you won't stay in the same place relative to the shadow, and will possibly experience gains and dips in brightness as you move past gaps in the rings. To illustrate:
The red dotted line shows the course that might be traveled by an observer standing on the planet's surface who is trying to stay more or less in the rings' shadow, as the planet spins around its axis over the course of a day. As you can see, in this particular case, there is a time around mid-day (just under that moon) when the sun edges close to a gap in the rings (i.e., the observer passes close to a gap in the shadow). From the surface, this would be experienced as a bright glow approaching from the southern horizon, and perhaps the edge of the sun beginning to peek out from behind the "cloud". Your nomads may want to time their travels so as to avoid any such gaps, or at least to encounter them around evening, when the sun is less bright. On the plus side, the timing of these bright spots will be a handy navigational aide to let them know if their travels are on schedule.
Of course, everything changes as the planet moves around its sun throughout the year. The rings move north to south and back again as the seasons change, growing wider and more curved as they move away from the equator and dangerously narrower as they move close. I'm guessing that your nomads are following the shadow of the rings because they don't tolerate sunlight well. In that case, there will be two times of the year which are difficult for them. During the spring and fall equinoxes, the rings will be oriented edge-on to the sun, and will probably not be wide enough to cover the whole disk. Looking up, you will see a glaring sun with a dark line through it, shining down with perhaps 90% of its full fury. At these times, it might be necessary for the nomads to travel only at night. Since they are by definition always staying on the winter side of the planet, these spring and fall times are also the hottest seasons of the year, even were it not for the waning protection of the shadows.
One more interesting thing: because the rings (Saturn's rings, at least) are largely made of ice, it's possible that you would get cool optical phenomena like this, if they're thin enough for the sun to shine through:
Expect this especially during the solstices, when the shadows (and the nomads) have traveled to near the planet's poles, and the sun passes through the rings at its most oblique angle.