The problem is that the panel has no content, so It doesn't show the background.
Try this:
<Grid>
<Button Width="100" Height="100">
<Button.ToolTip>
<Controls:MyToolTip >
<WindowsFormsHost x:Name="wrapper" Margin="0,0,0,0" Background="{x:Null}" >
<wf:Panel x:Name="previewScreen" BackColor="Purple" Size="200,200" >
<wf:Panel.Controls>
<wf:Label Text="Test"></wf:Label>
</wf:Panel.Controls>
</wf:Panel>
</WindowsFormsHost>
</Controls:MyToolTip>
</Button.ToolTip>
</Button>
</Grid>