True, but without light it's even harder. Of course we have seen life here around thermal vents but did it originate without light?

Light is not needed. Life on Earth got along fine without photosynthesis for hundreds of millions of years, and the hypothesis that life first appeared on Earth on the seafloor around thermal vents is quite plausible, even if we might never know for sure.

Life was also around here when the earth was a snow ball covered in ice.

Yes, although I think it's still debated whether there actually were any "total snowball" events or whether even the most severe ones still had open ocean near the equator.