You are right in identifying the river as an incredibly important symbol in this novel. One section that focuses on the river and how it operates in the lives of Jim and Huck is at the beginning of Chapter 19, which describes the peace and tranquillity of their lives together on the river. Note that this is also ironic as later on in this chapter they will pick up the Duke and the King who will disrupt this peacefulness and tranquillity.
In fact, this sums up how the river is used symbolically in the novel. One of the key divisions is the conflict between nature and civilisation. Whilst Huck and Jim are by themselves on the river, they live a wonderful life and are able to live free and happy. When they meet other humans, such as the Duke and the King, Huck is presented with the bad aspects of human civilisation, which is enough to make him want to escape being "sivilised" at the end of the novel and return to nature.
Note how nature and the river is presented at the beginning of Chapter 19:
Two or three days and nights went by; I reckon I might say they swum by, they slid along so quiet and smooth and lovely. Here is the way we put in the time. It was a monstrous big river down there - sometimes a mile and a half wide; we run nights, and laid up and hid daytimes; soon as night was most gone we stopped navigating and tied up - nearly always in the dead water under a tow-head; and then cut young cottonwoods and willows and hid the raft with them. Then we set out the lines. Next we slid into the river and had a swim, so as to freshed up and cool off; then we set down on the sandy bottom where the water was about knee deep, and watched the daylight come. Not a sound anywheres - perfectly still - just like the whole world was asleep, only sometimes the bullfrongs a-cluttering, maybe.
The description continues, and you would do well to read the rest of this section, but what is important to realise is that Jim and Huck are presented as living some kind of Edenic existence - it is just them and Nature, and they live very peacefully and in harmony with their surroundings. This is in sharp contrast to the picture of civilisation that is presented where humans trick each other, kill each other and even the "good" ones practise slavery.
I never felt easy till the raft was two mile below there and out in the middle of the Mississippi. Then we hung up our signal lantern, and judged that we was free and safe once more...Other places do seem so cramped up and smothery, but a raft don't. You feel mighty free and easy and comfortable on a raft.