I recently read that the adoption mechanic can be seen as closure to what happens to the kids at Honorhall, after our dear friend Grelod the Kind is slain.
The trailer shows the adoption of a street urchin, in what appears to be Whiterun.
But can we still visit Honorhall and adopt a kid? I felt so bad not being able to help them.

You would be able to. If not i would turn into a werewolf and kill the Other young girl not letting me, Then they would want to come with me

Concerns about the fate of the Honorhall kids was a large factor in the creation of the adoption mechanic. Ergo, I would be quite surprised if they were left unadoptable.

my guess is before said dark brother hood quest you can adopt kids from grelod the "kind"; with attitude of course and then after that quest from the young woman that over takes the orphanage.

should be sweeeeeeet.

I kinda want to adopt Aventus, kid needs a family.

screw those dirty nords
where are my elf children!!
i wanna raise my kid to be a thalmor agent, like my character