Given the Horse Lord expands the map quite to the east along the Siberian wastelands, do the hordes spawn earlier/in the middle of the map or they still arrive in the usual period and from outside the map? I have searched on the wiki, but it does not deal with this DLC explicitely.
So, as apparently noone has yet checked in-game, I went to look at the game files.
There is a new event (ID: 60500) with flag "mongol_empire_arrival" that takes the place of the sequence "mongol_horde_rumors/il_khanate_arrival/golden_horde_arrival". The new event trigger is in the year 1210 (so 5 years earlier than the previous event).
Also, no matter if you have Horse Lords or not, Temujin (AKA: Genghis Khan) spawns in "Ordu Baliq", ID 1457 (that apparently in game is known as "Kara Khorum"). With the new expansion changes only the name of the CB (tribal vs nomad invasion).
The information is contained in the "mongols_events" file.