Jaguars don't have bonus vs mounted. As for getting animal husbandry, that will delay your spearmen quite a bit if you don't have any horses. In addition, when do you think you can get Workers? If you can steal one from Aztecs early on, then that can work but getting easy horses is very rng dependent. With only 8 tiles with no forests, spearmen and Status of Zeus (which you can speed up with heavy tributes) with some Archers can help you a lot. Don't forget that you get a free Barracks from that Wonder so getting Drill I can make a difference too. Horses aren't that bad if you know you can get them and there's more rough terrain. Moving Spearmen through rough terrain means the AI has a better chance at getting Swordsmen and really halt your attack.