The mouse event goes to the TextBox that's inside the NUD. You can get a reference to it from Controls property, index 1 is the textbox:
Public Sub New()
InitializeComponent()
AddHandler NumericUpDown1.Controls(1).MouseDown, AddressOf NudMouseDown
AddHandler NumericUpDown1.Controls(1).MouseMove, AddressOf NudMouseMove
End Sub
This kinda breaks the rules but its okay, that control is never going to change anymore.