Saturn has a very low density and its gravity is not that much different than Earth’s, so I imagine you would initially free fall similar to how you would on Earth. The Saturnian atmosphere is closer to pure hydrogen/helium than other planet so your early visibility would be pretty good.
The drawback is you would not have a lot of sunlight to work with, so hopefully your excellent space suit would have powerful headlights.
When you started your descent the temperature may be as low as -250 C, but as you zip through the clear air to the first cloud layer the temperature climbs to -130 C. You are not falling that fast, your terminal velocity is around 200 km/h and will gradually slow as you reach thicker and thicker air, but so far you have fallen about 100 km and start passing through your first light cloud layer of ammonia crystals.
Saturn is a very windy place with the equatorial wind reaching speeds of 1,800 km/h, slowing somewhat towards the poles, but either way you are getting some lateral buffeting.
By the time you’ve passed through the second cloud layer of ammonia, hydrosulfides and ice crystals, the temperature is getting warmer, in the -70 C range and you have fallen for 170 km.
Another 130 km further and it seems more Earth-like, zero C or more and clouds of water, some of it liquid so you flip on your windshield wipers.
You have now fallen close to 400 km, and it’s taken over 2 hours, temperatures are climbing from freezing to as much as 80 C. Pressure is increasing rapidly now and you are seeing more and more liquid compounds, an hour or 2 more and the hydrogen is beginning to liquefy under the pressure. Helium is becoming more of the mix and temperatures continue to rise. Friction and static electricity generate lightning that arcs in from the troposphere.
As the liquid hydrogen thickens you continue to slow your descent until you have to fire up your propulsion system to proceed further. Eventually you see pressure liquefied helium as well and then a new barrier - metallic hydrogen which is much denser than water and crackles with magnetic fields it generates.
Other than increasing heat (up to 11,700 C) and pressure (>1000 bars) in this sea of metallic hydrogen you have a long way to descend until you finally reach a rocky core of compressed heavier elements like carbon, oxygen, silicon, and iron in a sphere possibly twice the diameter of the Earth.
Now the hard part….how in the hell are you going to get back out ?
