Could you clarify? Do you want the search option open to be able to search all group discussions at once, from all groups, or have a search at each group individually?
There's no way a search option could return all group discussions at once, since many groups are private or do not allow non-members to view discussions.
Groups have minimal features at this point, which, judging from previous website development by this team, are sure to be fleshed out in the future.
Personally, the most frustrating missing feature in groups is the ability to search the threads for something I remember being posted in the past. But that is such a minor issue compared to launching the game that I didn't post about it.
Getting group lodging ready for in-game play is likely to be much higher on the group features to-do list.
I mean searching within the discussions of a specific group, just like you can search the forums. I would like to search the discussions to see if something is already discussed before I create a new thread.