You can and will most likely end up in some of the Slav defense variations. It is also OK against c4 or b4 or pretty much anything else, since c6 prepares for d5 afterall.
Can you play caro-kann aginst d4?
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Caro-Kann is a response to e4. If the opponent starts with d4, it will be a different opening (and there will be much better responses than c3).
My go-to defense in black pieces is caro-kann but is it good to play against an d4 opening or does it just make sense against e4? (I misswrote the topic sorry about that)