If you can run it through a grinder, okay. But the cedar is not only woody, it is oil-rich/resinous and so left alone it will be VERY slow to break down. You can add some, but don't over do it.
In general, we suggest no more than 10% of a pile be any one ingredient. Part of the point of composting is to have a balanced mixture.
Read the browns/greens sticky at the top of this section for more suggestions of ingredients.
Do you save all your kitchen scraps? I put a two gallon bucket of kitchen scraps in the compost pile every week, year round.
If you go by Starbucks type places, they will give you lots of coffee grounds (I bring home the grounds from all the coffee that gets made at work).
In the fall, I bring home bags of leaves that other people put out at the curb, so I use fall leaves as my main "brown" much of the year. When the brown paper yard waste bags the leaves come in are empty, I compost those too.
Pulled weeds, grass clippings, deadheaded flowers (every spring I dead head the huge old lilac bush in the front yard once flowers are done, that fills up my compost pile for a while) , paper grocery bags, torn up cardboard boxes, used paper towels, toilet paper tubes, yard trimmings, sawdust, wood ash (in small amounts) .... anything organic.