Can I plant in Winter?

My temperature zone is classified as arid/cold arid. I live in South Africa, in the Karoo area.
Planting in winter is a no-no here. If I plant some seeds in a domed seed tray, perhaps also domed cuttings? atop a towel in my garage, would it be feasible?
Or should I rather wait it out?

You're pushing it, just living yourself where you are, having made many accommodations for survival. Any plants you introduce need the same. Native plants can probably be planted in flats anytime and just left to the elements.
Everything else probably should be started in the same conditions that would exist in their homeland. If they are temperate, they could left in flats outdoors and germinate next spring, but would have to be watered when the temperatures would support germination, before you see them emerging. Except. Your photo-periods are always going to be much more conducive to triggering germination earlier than your nighttime temperatures would nurture. Long sunny days with deep freezes overnight will kill many seeds before you see any action above ground. Normally, temperate seedlings should have an average of ~50°F overnight when they emerge. You need to provide these conditions to be safe.

They are all native. They can resist frost (as trees) but I also feel the cold air might kill them (as seedlings). The thing is just I didn't want to wait until spring again, thought I could do something in the meantime. Generating heat is a costly thing and I don't want to go through that. I will wait it out then.. Thanks..

Just follow what they do in nature. Seeds in nature fall of the tree in autumn, and lie in the soil until the spring. Trying to create a spring environment in winter will be difficult and probably frustrating.