I just purchased a 2horse bumper pull, 2800lb empty, will be pulling 2 horses, no more than 2500. Some people tell me I will be fine w/ a 1500 truck others say go to 2500. Trying to keep price down since I will only use vehicle about 15 times a year for towing only. Considering Dodge ram 1500 5.2L 4x2 (7500 lb tow/ 12,500 CVWR), truck weighs 4470. VERSUS 2000 chevy suburban 1500 4x4, tow 8800 weighs 5123, not sure of CVWR. The ram has an 8.7" longer wheelbase, which is a plus. Anybody know the suburban CVWR or have an opinion on this? All my numbers are from what I could find on the internet, so I hope they are right. From my calculations the Ram should still give me 2000lb to play with in terms of equipment and people in the truck. Need CVWR of suburban to figure that out.

Welcome to the forum. Yes, a 1500 truck will be able to pull your horse trailer. You will right on the cusp of GM & Ford recommendation of a WD hitch. (5,000#+, a WDH is recommended)

Having horses, usually means hay, shavings, manure, and other heavy/bulky items to be hauled. 40 bales of hay is too much for a 1/2 ton p/u but a 3/4 ton p/u will handle it better. That's why you're getting the nod for a 3/4 ton from people.

Thanks, that's what the expert tells me (who's written a book on this), but I'm still troubled by experienced horse people who tell me stories of dangerous swaying and less control w/ the 1500's, even with sway bars. Safety is my #1 concern, and if I need to spend a couple of thousand more for a 2500 I will do so if it's safer. I'm not going to be carrying more than 1 hay bale to horse shows, which is the only use I'll make of this truck/trailer combo.

Sounds like you're leaning toward a 2500 truck anyway. I think, the 2500 will be better suited for your needs. The 2500 will have heavier tires, suspension, gearing, etc. The stiffer tire side wall will add to the stability.
Also sway bars are not the same as a WDH. The difference is a sway bar only damps the sway motion between the truck and trailer. A WDH will transfer some of the weight from the rear tires to the front tires. Then the front tires have more traction to resist the sway motion around the rear tires. That additional traction also provides more steering control.

While you already have a BP trailer, If you decide to purchase a truck, you'll be ready for the ultimate in horse trailers... a gooseneck. There isn't a question of sway then. I used a BP trailer once, then have been a GN trailer owner for the last 22 years.