**UPDATE**
So since this issue first came up, I have had it into the dealership 3 times now. It has been at the dealer this most recent time for over a week, and they just told me they need yet another few days.
First, they said it was just that the fuel filters needed to be replaced. I disagreed, but that didn't go anywhere. Since they had just sold it to me a few weeks prior, I was able to convince them to cover the charge, even though filters weren't technically an "under warranty" item. They gave it back to me and sent me on my way. The very next time I drove it on snowy roads (maybe 2-3 days later), the light and single chime came right back on, so I brought it right back to them. This second time they said it was the fuel filter housing itself that needed to be replaced. This time, they covered the cost under "warranty", replaced it, and sent me on my way. Well, the same thing happened again a few days later, so I brought it in yet again - obviously very upset by this point. This third (most recent) time, the first thing they said was that the "connector" for the sensor itself needed to be replaced. They had to order the part and it would take a few days. A few days pass and I get a message that the wrong part came in, and that I needed to wait another day for the correct part to arrive. Well, that part came in, they replaced it, and I told them that I would not take the vehicle back unless they took it through a car wash to emulate the rain/snow situation. They agreed, and of course, it came right back on when they took it through the car wash. Now they are saying they need to replace the entire chassis harness/wiring (and sent me the picture below of what I was able to find as Mopar part 68521690AA).
On top of all this, I contacted Ram Customer Care and the person on the phone opened a case and said that a case manager would reach out to me and work with the dealership. That person emailed me the next day to say that they were going to work with the dealership. I didn't respond, as I assumed that it was just a courtesy email to introduce themselves, and that they would respond again with their findings or any updates. The next email I got was 3 days later saying that since they didn't get a response from me, they closed the case. I have responded back to the person 3 times since then and have gotten nothing back.
Needless to say, this has been a hell of a headache! The positive is that they sold me the used Ram with a 3 month 4,000 mile warranty (I just bought it used at the beginning of the year with 44,000 miles), so they have covered all of the costs so far. Obviously, the negative is that they seem to just be replacing random things one-by-one trying to see if each thing fixes the problem, without actually knowing what is actually causing the problem. The old "throw sh*t at the wall to see if it sticks" approach.
I believe, once this is all over, they will have had the truck for more time than I have so far...
Here's to hoping the chassis harness/wiring is the real culprit...