The Armada should have around 9500 lbs. of towing capacity, if it has a tow package.  If it doesn't, it's around 8000lbs.  I have a Titan, and found it to be very reliable when towing.  While it is still a 1/2 ton truck, it still should be enough for you to tow and stop your 3h bp.  Denali's should have around 8800lb capacity.  I personally don't know anyone who tows with one, so I have no opinion on that.

Regardless of what you choose, you do need to remember that you are "towing" everyone and everything thats inside your vehicle plus whatever is attached to your hitch.  Many people forget that.  You will also need to consider the topography of where you are towing when choosing  your tow vehicle.

Personally, I would know the weight of the bp, horses and people/stuff that will be riding in the vehicle and subtract that from your tow rating.  If you have less than 1000lbs difference, I wouldn't tow with it.  Being able to stop safely is very important.

SUVs can do a very good job of pulling a trailer. With most 3HBP SL trailers, you can shift your loads to help balance the trailer and lessen the tongue weight on the towing vehicle. This usually is not available on 2HBP ST trailers.

The longer the wheelbase of the SUV, the more stable it will be. Suburbans, Expeditions and the like have done well towing for many years. The vehicles must be adequately prepared for towing. This would include the largest motor and a proper rear axle ratio. Aux transmission and engine cooling systems are usually included in "towing packages", which should be considered absolutely manditory. Factory installed receivers are the best and are usually part of the packages. Some also include larger brakes, more robust tires and suspension systems, including automatic air height adjustments.

I wouldn't purchase a sway bar system until your rig is on the road and tested. With radial tires installed, most properly loaded trailers track quite well, without needing any auxillary mechanics. Every situation differs and you can't really know yours until you try your first pull.

One of the most important trailer installations components will be an electronic brake controller. Your trailer brakes will be expected to stop their load. Proper brake timing and the strength of the application is paramount. You cannot safetly pull, whilst expecting the towing vehicle to provide all of your braking effort.

A properly prepared SUV can be a good multipurpose vehicle. Just make sure to tick off the options list for the specifics you will need.

Thanks so much for the info.  I have a 3500 diesel dually quad cab for pulling the big LQ 3h trailer.  I currently have 3 horses however one is pregnant so next year we will have 4.  Don't want to upgrade the trailers so I figure this is the best alternative.  Will be needing to trade in the car soon anyway so ...

I live in Florida near the NW gulf coast.  With hurricane season here in full swing it brings to mind that being able to evacuate all animals is essential. 

Will take all of this into consideration when the time comes to go shopping.  Hopefully soon!  Although I do not like the idea of a vehicle payment at all!  I'm not disciplined enough to be able to do it otherwise evidently.