Like most of the other pieces of a Cats costume, there are several ways to make the warmers. You could sew them from fabric and color them, knit them, buy them, or crochet them. It depends on your budget, skills and time.
Sewing looks the least authentic. However, it is fast, and requires no knowledge of knitting or crocheting. Just cut a rectangle out of your fabric (a fuzzy fabric might look more authentic) that is a little longer than you want the warmers to be, and is a bit wider than the circumference of your arm or leg. On the top and bottom, fold over a little bit of fabric and sew it down, to make a tube for elastic. Thread elastic through these tubes, then fold your rectangle over lengthwise and sew down the sides (do not sew the elastic tubes yet). Put it on, adjust the elastic, tie a knot in it, then hand sew the tubes closed. Color the warmers with fabric markers or dye to match your character.
You might try buying an old white sweater from a thrift shop and using the arms to make arm warmers and the body to make leg warmers - the knitted fabric may look more authentic. I haven't made a finished set of warmers this way, but I did sew them up, and it will work, but the success of it will depend on the sweater you buy and how it's knitted.
These, I crocheted:
I definitely like the crocheted ones better, they look more authentic. Basically, you have to have some knowledge of crochet, and some time. Start by making a chain in the yarn that will go around your arm with the fit you want. Then when you start the second row, connect the ends of the chain - now you have a loop, which as you keep going, will become a tube. You can increase and decrease the rows to shape it to the fit you want. This will be easier the more experience you have, I imagine - I'm not very good at it myself, so it was a bit tricky.
I recently learned how to knit, and knitting goes reasonably quickly once you get going. However, I've never knitted warmers myself, so I really don't know how it goes (I don't even know how to knit a tube - just a flat rectangle). Knitting does turn out some authentic looking warmers, so if you know how, this is probably the way to go.
I haven't bought warmers because for the most part, they look too thin. You can find them at dance supply places, and generally, they do come in white, but to me, they look to insubstantial for most characters. They aren't usually very expensive, depending on where you find them. You would have to color them with markers, dye or paint.
Find more information about making warmers here: