Don't worry about the 3.55. With the 6 speed tranny, use tow haul and "bump" to 5 or 4 when required and you will be fine. As for hills and your trailer, find me another gasser that would do it any better.
Went to the RV show in Regina and noticed the same thing. There were 2 pups when ususally many more. IN fact, there were very few smaller trailers (HTT or other wise) at all. Lots of light wieght trailers in bigger sizes.
I had 17" wheels on my 2010 Ram and put Goodyear Silent Armour LT tires on when I bought it. Loved the tires. They are one of very few (if any others) LT tires that area also winter rated (not just M&S but in fact winter rated) . Seeing your from BC, these would come in handy. Loved how they handled the snow and ice especially on our annual ski trip to Panorama.
My 2012 ram has 20" wheels and I wanted to put the same tires on when I bought it. However, the goodyear silent armour LT's do not come in 20" size. I went with the P rated silent armours as they have a stronger sidewall than most P rated tires.
I do agree that the stock tires that came on the 2010's and 2012's (good year HP on the 2012 and goodyear SRA on the 2010) are good for a quite ride but that is about it. That is why I swapped mine out at time of purchase.
I had 9/32" of tread (new they have 13/32”) on my 2010 at 48,000klm. They wore really well and still gave a great ride. My Lt's were 6 ply not the 10 ply but based on your trailer weight you would be fine. I have yet to tow with the new truck and the P rated tires but I do not expect much trouble.
As you probably know, it is not so much the weight of the trailer, but the weight on the hitch. There is not much payload for the RAMs. A 10,000 lb trailer should have about 1300 lbs on the hitch. This alone will either put you at your payload or over. That is without anyone else or anything else in the truck. You may be at your max already with your current trailer once you add passengers and "stuf" in the box of the truck.
I too had a 2010 RAM quad 4x4 with the 3.92 rear end. Great set up.
I have had a 2004 Ram 1500 4x4 quad cab with 3.55 rear end and it towed our trailer OK. Moved up to a 2010 Ram 1500 4x4 quad cab with 3.92 and 5 speed tranny. The tow was very much improved over the 2004. Currently have a 2012 1500 4x4 crew cab with 3.55 and 6 speed tranny. Even with the 3.55 rear end, the 6 speed tranny makes the towing much the same as my 2010. Nice part is the "bump" shifter (which your 2010 should have) where you can lock into 4th if need be and away your go. For the most part, I am able to run in 5th without much (if any hunting). Our trailer is a 19' shamrock hybrid. Two kids, wife and box full of bikes and golf clubs and we have no problems. YOu have lots of power, but will be limited on payload. I also put LT tires on my 2010 (17" wheels) and could notice the improvement without much side to side motion. Current wheel size is 20" and could not find the LT tires in this size (tires that I wanted anyways).
My 2010 and 2012 Ram do not have an air filter but there is space for one. Just pop your glove box out and the space for the filter is right there above the fan motor. If you do not have a filter door, you do not have one. If you want, there is a kit that you can buy and cut a door in and insert a filter. Follow this link http://www.youtube.com/watch?v=l0TyhcRaAsA or this one http://www.ramforum.com/f75/cabin_air_filter_mod-12200/