Why won't this script that is placed in a GUI remove the players face and replace it when clicked?

The problem is h. Variable h is the character. Not the head that the face is it. You also need a ) after the end. This is because the function is in the connect. This is a shorter way to write event scripts but you need the ). So basicly you just need to close the parentheses. Here this is better:

player = game.Players.LocalPlayer
h = player.Character.Head
script.Parent.MouseButton1Down:connect(function()
h.face:Destroy()
--No wait needed.
local newface = Instance.new("Decal",h)
newface.Head = "Front" 
newface.Name = "face"
newface.Texture = "http://www.roblox.com/asset/?id=138224650"
end) --You need the ")" because of line 3.

Hat:

player = game.Players.LocalPlayer
h = player.Character.Head
script.Parent.MouseButton1Down:connect(function()
    h.face:Destroy()
    for _,v in pairs(player.Character:GetChildren()) do
        if v.ClassName == "Hat" then
            v:Destroy()
            game.ServerStorage.Hat:clone().Parent = player.Character --Put the hat in ServerStorage and name it "Hat".
        end
    end
    local newface = Instance.new("Decal",h)
    newface.Name = "face"
    newface.Texture = "http://www.roblox.com/asset/?id=138224650"
end)

EDIT:

For multiple hats and this is both of the scripts combined

player = game.Players.LocalPlayer
h = player.Character.Head
script.Parent.MouseButton1Down:connect(function()
    if not h.face.Texture == "http://www.roblox.com/asset/?id=138224650" then
    h.face:Destroy()
    for _,v in pairs(player.Character:GetChildren()) do
        if v.ClassName == "Hat" then
            v:Destroy()
            for _,i in pairs(game.ServerStorage:GetChildren()) do
            i:clone().Parent = player.Character
            player.Character:MakeJoints()
            end
        end
    end
    local newface = Instance.new("Decal",h)
    newface.Name = "face"
    newface.Texture = "http://www.roblox.com/asset/?id=138224650"
    end
end)

Hats:

p = game.Players.LocalPlayer
char = p.Character
Storage = game:GetService("ServerStorage") --Using :GetService() because the script can cause an error if used in multiplayer(uploaded to roblox) when not calling the service

script.Parent.MouseButton1Down:connect(function()
    local cont = char:GetChildren()
    for i,v in pairs(cont) do -- Removing all other hats
        if v:IsA("Hat") then
            v:Destroy()
        end
    end
    local hat = Storage.HATNAME:clone() --Change HATNAME to the name of the hat and put the hat in ServerStorage
    hat.Parent = char
    hat.Name = "Hat"
    --If the hat is not anchored in ServerStorage it should appear on your head.
end)