Reuse the lanyard (with clips on both ends) that you've got with your conference/expo/fair badge by turning it into mitten clips for your toddler.
Just thread the lanyard through the sleeve of the child's jacket, through the loop (or sew it on to a collar) and then through the second sleeve (see the picture below). Clip the mittens on.
The lanyard is long enough for a child under 4 years old.
How to reuse an event badge