It is possible, you even have what are called zentai suits. They can come in all kinds of colour and textures. Though the head and such will be a problem. However, it is not all that impossible as one might think.
It will already be a bit bulkier than the person wearing it. But one can also create the illusion a character isn't bulky, this doesn't mean you need a morphsuit or something. Especially if you have a good fursuitbuilder that is able to make it look good