On nice days Phoenix goes out in her backyard pen, but it's still a little cool outside for a lone goatling. So, I turned the leg of a pair of thrift store sweatpants into a coat for her. (You can use a sweatshirt arm for this too; the cuff might only fit a younger/smaller kid though, or you might have to cut through the cuff so it isn't so tight.)
The elastic or bound edge of the ankle or wrist will be the neck of the coat. Hold it up to the side of the kid, and mark where her back ends and tail begins. Cut the leg (or arm) off the garment at this point. I cut it a bit longer to leave some wiggle room and grow-into-it space.
Hold it up to the kid again, and mark where the leg hole should be on one side. Mark the front and back of the leg hole, and cut out.
Be generous, an active kid needs an unrestrictive leg hole. Then flatten the coat on your table and cut a matching hole on the other side.
If you attempt to try it on the goat at this point like I did, you'll find out that it's impossible to get the head and neck down through that long tube shape! I had to cut the belly out of the coat before I could get it on her. I free-styled that cut. Her umbilical cord is gone (she's a month old now), but if you are making a coat for a young kid or a buckling, make sure you make this cut-out large enough.
Then it went on much easier. How to: put her legs in the holes first (even this is easier said than done), and then gather it up and slip over her head like you'd put on a turtleneck yourself.
One warm goat kid!
A sweatshirt or pair of sweatpants will of course yield two goat coats. How about a trip to a thrift store?