While @chapoi is definitely the Horizon expert, I will jump in since she’s on leave for this week.
Horizon does not support any tag display on the topic cards, so it is not compatible with Tag Icons. We are considering adding support for displaying tags on topic cards, which may help move things in the right direction for you, but I am not certain that will cover Tag Icons since that component is really built around the tag display that works on Foundation and in the “table style” topics list.
So there’s a good amount for us to figure out here. At this point I’m not sure when we’ll know more — at the earliest, it’ll be sometime next week, but it will likely be later than that since we’ll need to go through some design work here and attend to other priorities, too. But we’ll follow up here once we have more to share!