Main difference is hot wallets are connected to the internet while cold wallets are not. Most people who hold digital assets have both (cold and hot) wallets because they are designed for different purposes.
Hot wallets are like checking accounts while cold wallets are similar to savings accounts.
People who have digital assets keep a small amount of money in their hot wallet for perchases or smaller buys. They keep the vast majority of their digital coins in their cold wallet. Maine reason people have cold wallets is so hackers can not steal digital assets that are not connected to any network.