It would be a lot easier if it wasn't on to a T-shirt, but this is what I would do:
Wash the T-shirt to shrink it before using, otherwise it will shrink after and the design will look funny. Draw the outline of the unicorns onto the t-shirt so you know where to place them. You can do that with a pencil and a light box. For a cheap light box you can make a light box with a piece of glass and anything that will hold the glass high enough to put a small light underneath and the light can be one of those that you press on to turn on and off in the closet. Before you draw make sure you iron some interfacing on the back to stabilize the shirt, otherwise drawing will be impossible.
Trace the horses onto freezer paper and cut templates. Make templates only for the parts that will be made out of the different crazy fabrics, like the body of the unicorns, the horns, and even the mouths and eyes. Make sure the fabrics have fusible on the back. Cut the templates out of the fabrics you want to use and iron them onto the t-shirts, right on the marks that you did before.
Make a satin stitch around the applique. Use black thread to make it stand out and look cartoonish and to clearly separate the parts, like the eyes and the body, etc. I would add another layer of fusible interfacing to protect the satin stitches from coming apart during washing. I would then load black thread on the top and bottom of the machine and free hand stitch lines like the eye brows and frown, lines of the ears, muscles of their bodies, separate the teeth and define the smiles and jaw lines. If you cut the eyes out of white or white on white you can then mark with a pencil where you want the pupils to be and stitch them freehand to make them look crazy.
Your greater challenge will be to keep the t-shirt open to do all the stitching, but if it a shirt big enough you should have no problem. Just make sure that the fabrics are washed as well. I usually don't wash first, but you don't want the fabrics shrinking or bleeding after so much work.
It sounds like a real fun project.
Maria