I'm not sure who mentioned anti-sway bars but I would suggest them as they don't hurt to have as extra insurance for stability
A lot of people get weight distribution bars and sway controls mixed up. They are two different beasts:
Weight distribution bars:
There are weight distributing hitches that mix the two (add sway control as well as weight distribution) but they're arguably overkill for a horse trailer as the weight distribution of a horse trailer doesn't lend them to having sway problems to begin with the way a travel trailer can. Inadequate tongue weight is the biggest reason for trailer sway, but it's almost impossible to load a horse trailer heavy on it's tail as can happen with a travel trailer when people load gear incorrectly.
A weight distribution hitch is far more important than a sway controller for a horse trailer, especially if being pulled with a tow vehicle with a light capacity rear axle...such as a half ton. As a side effect to proper weight distribution the vehicle combination becomes more stable (rear tow vehicle wheels not squashed and squishy, for example) so the setup becomes inherently more stable as a simple result of that alone.
I have to agree with this advice: "One thing that might help in your research is taking your vin number off the suburban in to the dealer, and they can print you off a sheet that tells all the options that come on your vehicle." by Altaleft.
It won't tell you much beyond what the OP has already told us other than about options that are not relevant to towing. The OP mentioned it has the tow package (which includes a tranny cooler amongst other things) and that the rear gearing is 3.73 which is also an important consideration with towing..but we already know those facts. The same option codes that a VIN search would result can be found on any vehicle by looking at the RPO sticker usually located in the glovebox:
All those codes indicate options and specifications. If you decode them it'll tell you everything about your vehicles options and outfitting from the factory with no need to run the VIN.