Splitting BTC and BCH from cold storage using bitcoin core wallet sending to exodus
Did you import the keys from your bitcoin core wallet to the exodus wallet?

It seems to me that you simply transacted your bitcoins to another adress (+Wallet).

This however does not mean that your bitcoin cash will also be send to that adress ( unless there was no replay transaction of course.(Which there is))

Your bitcoin cash is still at the adress where your bitcoin was at the time of the split.
Import that adress ( or rather the private key) into a bitcoin cash compatible wallet and you should see your BCH balance.