No. G1 and G2 only had ponies, pegasi and unicorns (plus some odd winged unicorns that were animation mistakes). The various cartoons also introduced human friends as well as a solitary dragon, mud-monsters, spiderlings, bushwoolies (don't ask), porcines, zebras, goats, flowerlings, monkeys, bulldogs and leprechauns as the antagonists.
G3 introduced a raft of new animal friends including ladybugs, birds, and mer-ponies but no griffons.
G4 then introduced all sorts of other animals such as cows, adult horses, griffons, cats, deer, Klugetown monsters, mermares, hippogriffs and Transformers (both Autobots and Decepticons).