So, according to the Wikipedia page on Saturn's rings, and this handy "optical depth" to transmittance calculator I found, the amount of light blocked by Saturn's rings varies.
- C ring; ~12% - nearly transparant
- B Ring; ~40~60-100%, Structure varies heavily.
- A Ring; ~40~60-50%90% - Heavy overcast day?
Now - Saturn's rings are mainly water ice, with some dust. Therefore they couldn't exist around an earthlike planet as it would be too close to the sun, and they'd evaporate. For the purposes of this question though lets assume they're actually made of rocks and dust.
They're casting a pretty deep shadow on the planet below, although bands of sunlight do break through from time to time given the structure of the rings.
Assuming the rings are around the equator, and that the planet has a similar axial incline to Earth, this means the ring-shadow would occur during winter. The hemisphere that is closest to the sun at the time would be out of the direct line between the sun and the rungs, and receive normal light.
Based on that, I predict you'd see a much heavier reliance on the wintering strategies we already see here on Earth:
- Hibernation/Torpor
- Migration
- Food storage/hoarding
- Fat supplies
- Antifreeze blood (depending on temperature drop?)
Summer would be relatively normal, whilst winter is harsher than it already is. Most large animals would need to employ some sort of wintering strategy to ensure survival, perhaps more than one. Plants would likely use tubers to store nutrients.
The land near the equator would be even more prime real estate than it is now, because as you mentioned, besides the poles it's the only area not affected by the rings. Depending on the opacity of the rings, life may be strongly focused near the equator