Loadscreens must exist on the client computer (your players machines). So, you have to provide them to your clients. This is true for all graphics actually. Doesn't really matter what graphics you have on the server side, the image that the player sees comes from the players computer.
The way the engine is designed, it is setup so that as little as possible comes from the actual server, meaning the smallest possible data flow from server to client. Scripts, creatures, npc's etc, are server side, the physical layout of the areas as well. But the server only sends the wok data to the client, the actual images (tiles etc) are loaded from client computer. As mentioned, the wok file is the only file actually transferred from the server directly and all of the controlling files, like 2da etc are controlled by the server.
Anyway, you have to send the clients a hak with the updated loadscreen.2da file, and the physical loadscreen image files as well. 2 per loadscreen, small version and full size version. Although technically, the players/clients only need the full size version, as the smaller version is only used to create/choose from when building the area.