1.) When I made some felt horses, I cut pieces of yarn double the length I wanted the mane to be.
2.) Then I folded each in half and threaded one at a time (folded end first for about 2") through a large-eye needle.
3.) I sewed partway through the spot (in and immediately out, just until the folded loop came through) on the neck where I wanted the yarn to go, removed the needle from the folded yarn and drew the two cut ends through the loop and pulled tight.
Basically, what I was doing is creating a slip knot with each yarn piece, kind of like rug hooking. It worked well for the mane.
The tail can be done in the same way, if you don't have too many yarn pieces, otherwise the slip knots are too bunched up and look messy. When I made mine, I created a tail by measuring about 6-8 pieces of yarn (double the length of my desired finished tail) and laying them atop each other, then tying an overhand knot in the center. I sewed the tail in place in the seam when I was putting the body together, making sure the knot was inside and sewn securely. The knot keeps it from being pulled out later.
Your projects sound great, especially the unicorn! I know you're kids will love them.
~ Kathryn