I’m using DAVdroid on a HTC One X with Android 4.2.2 and sync with Horde.
While syncing calendar works fine, contacts are not shown in the contacts app.
I’ve seen the HTC issue in the FAQ but I think this is something different.
I tried Contacts Editor Free to create a contact and this one appeared in Horde. Thus it seems that the synced contacts are one the phone but somehow not shown in the contacts app.
The app has a “multiple source” dropdown menu. The DAVdroid account is not shown here, but only SIM, phone, Google and Google+. It seems the app does not recognize the DAVdroid account?!