I would strongly advise against it. The oils from the Thuja species (of which western red cedar is one) is known to be toxic and cause convulsions when people have used it in remedies and the dust causes a lot of allergies and industrial asthma. But I'd be more worried about how it would affect the wine even in very small quantities. Cedar doesn't appeal to me as a flavor in wine and there's a reason why oak is usually the only wood that touches wine.
Like most people who do a lot of things at home I like to use all my waste and keep sawdust and wood shavings for all kinds of things like thickening epoxy and maple or hickory and some other woods go into the smoker or bbq. Not quite sure what to do with cedar though as I've never had a heap of it around to work with. There'd be guys on here that know more about this stuff than me so happy to be corrected if I'm wrong. But I'd hate for you to ruin a batch of wine or even worse make yourself sick.
I'm down here in the Texas Hill Country we have a lot of cedar and wineries. I'm not fond of a lot of Hill Country wines as I taste cedar. Now folks say I'm crazy and that is all in my head. My taste buds, say otherwise. In my case it is most certainly cedar pollen on the grapes.
Plane down some cherry wood, I like it in a malbec.
I use Scott Tannin FT Rouge exclusively. "Scott 'Tannin FT Rouge is composed of exotic wood and chestnut tannins." I would not use any form of cedar in winemaking unless you have a problem with moth's getting into your wines.......