As a general rule of thumb it's usually best to keep coins in your own wallet unless you're trading with them. But for the wallet we released today, no such action is needed. All exchanges will be switching to the new wallet on their end.

By the time we start moving to the new PoS chain, you will first need to withdraw your coins to your private wallet before sending them to the Exodus address, since you will need to be able to use your private key to claim them on the new blockchain. However, this is not relevant yet right now.