Is it safe to use the same address I connect to Horizon Market in other wallets or marketplaces?

No, it is not safe and it is strongly discouraged. While Horizon Wallet prevents spending UTXOs with attached Counterparty assets (unless the user explicitly allows it), other wallets or marketplaces that do not support Counterparty can and at some point very likely will spend those UTXOs as part of normal BTC transactions. When these UTXOs are spent, the assets that are attached to them are sent with them and cannot be recovered.

There is a number of different ways to minimize the risk of accidentally spending your UTXO-attached asset balances, but the simplest thing to do is to have a dedicated wallet that you use with only Horizon Market (or at least a dedicated account in your wallet). Of course, if you use Horizon Wallet, there is no risk of accidentally spending your UTXO-attached balances at any point (as long as you don’t share the Horizon Wallet seed or address private key with another wallet).