I've learned that most exchanges and wallets support the Segwit chain now, but some do not (Exodus, for example).  Will I run into any issues transferring BTC from, say, Coinbase (Segwit) to Exodus (non-Segwit) to Ledger (Segwit)?  Will the middle link (Exodus which is non-Segwit) mess up the transaction in any way?

See here for Exodus wallet roadmap, scroll all they way to bottom. http://support.exodus.io/article/96-exodus-wallet-roadmap