So, the darkspawn are Thedas' equivalent to orcs, goblins, ogres, and self-controlled undead (like ghouls and ghasts). Lower levels of these creatures are considered "Minor" threats within the game rules, which is an acceptable challenge to 1st-4th level characters. Darkspawn are mortal creatures, but are born with the taint of the Blight (and some can infect others); a person who is infected with the taint, if they survive for any length of time, become "ghouls," and eventually seek out darkspawn to serve them. They really are the bogeymen of Thedas.
Most are in the Deep Roads, and the dwarves are in an eternal war with them there (the First Blight nearly destroyed dwarven civilization).
Traditional "zombies" and "skeletons" are represented by spirit-possessed corpses. In Thedas, since this is always a possibility, the dead are cremated in a funeral pyre. Animated corpses more prevalent on ancient battlefields and other places away from civilization, where the dead are likely to receive no such treatment.
Here's a link to Spirits in the Dragon Age wiki:
https://dragonage.fandom.com/wiki/Spirit
And, yes, darkspawn seek to destroy things and taint all they see. A chance encounter with them is usually rare, but possible, especially in places where caves may extend deep into the earth, or ancient dwarven surface entrances. Given that you're within walking distance of those dwarven steps, it's possible an entrance to the Deep Roads has recently opened up there.