Have you looked at the client logs in the console for errors? (F9 in published game). With FilteringEnabled on, you can weld things to your character from a LocalScript, the difference is that only you will see it. Because not even you are seeing the item appear on your character this suggests something else is wrong. One possibility is this line:
local face = game.ReplicatedStorage.BearFace:Clone()
This can fail in a published game if the line of code is encountered before BearFace has actually replicated to your client. In this case, you should have a red warning in your client logs. You need to wait for BearFace to replicate before trying to clone it. This can be as simple as
local face = game:GetService("ReplicatedStorage"):WaitForChild("BearFace"):Clone()
But… if you want everyone to see your character wearing the face, this point is moot, you need to clone the part and weld it from a server Script. This means sending a RemoteEvent from your client to the server to request the face be attached to your character.
But there are other options if you need to avoid a blocking call.