Four Legs Good, two legs bad
There was an old saying that "the most dangerous animal in the forest walks on two feet" ~ it is a reference to mankind.
Your setting, being more or less a temperate Eurasian analogue, is nicely suited for the greatest danger to the characters (potentially) being other humans that the party encounters. Bandits / brigands / outlaws, fanatics (like the White Cloaks of Robert Jordan's Wheel of Time), mercenaries guarding a caravan who assume the party to be a small band of brigands or bandits, cattle rustlers who hold that "dead men tell no tales" and are armed, smugglers, various pastoral peoples guarding their sheep/cattle/horse herds' grazing areas, adventurers, assassins, deserters from an army, rangers protecting their lord's forest or livestock, outriders and scouts keeping the local duke's territory safe from wandering miscreants (which the PCs are assumed to be), servants of a magus or a cult leader seeking new victims to experiment upon or sacrifice (respectively), border guards with permissive rules of engagement and itchy trigger fingers - these are all potentially canny and dangerous opponents who are "the beast that walks on two feet." They are also encounters that may be resolved without resort to bloodshed. 1 This makes them quite flexible as a tool for the GM. (A substantial portion of the encounters I ran when I GM'd Empire of the Petal Throne ended up being other humans, encountered near or on the Sakbe roads, although plenty of more monstrous encounters were to be had as well).
Optional lizard peril
For an occasional Jurassic Park feel, you can introduce a lush valley where packs of small to medium sized dinosaurs roam about looking for a snack. Similarly there is the threat of soaring lizards such as pterodactyl flocks - that can pose another hazard from their nests in the hills / cliffs / mountains. (Substitute in giant eagles or rocs looking for fresh meat to feed their chicks and you've got most of the aerial hazards covered but those are more 'fantasy' than not).
Disease (an option)
A character getting sick doesn't usually make for a great adventure, unless you can morph that threat into a "Arglbargl is sick, we must find a cure" which leads to other encounters where someone has to "cut the heart out of a yak and boil it in a snow panther's gall for an hour before you feed it to Arglbargl" as a cure. This would necessitate meeting a local shaman/healer/wise woman who offers that cure as the only way to save them from the wasting disease.
Snakes at a river crossing
A very memorable scene / vignette from the mini series Lonesome Dove included a river crossing where there was an infestation of cotton mouths / water moccasins posed a lethal threat to horses, cattle and men.
Four legs good, two legs better
Now and again herd animals will stampede. Anyone and anything in their way is in peril. Use of terrain and / or use of their wits is how the party will evade/survive such an encounter (or possibly perish if a TPK is a potential for your table).
Hungry packs of predators/scavengers
Hungry wolf packs or hyena pack who outnumber the party can pose a threat to them.
Wild boars, javelinas, feral hogs
This is something of a RL hazard near to where we now live, and other places where we have lived; wild boars, javelinas, and feral hogs all have a mean streak that can trigger when disturbed or threatened. They are also cunning and smart, as animals go.
Every so often Army Ants swarm forth and plagues of locusts ravage the land. Characters caught in such an event must deal with it or potentially perish.
1 As but one example for one game, the AD&D 1e Monster Manual had listed under the variety of "Men" the following kinds: buccaneer, berserker, pilgrims, dervish/nomad, merchant, caveman, tribesman, bandits and brigands