According to their terminology, an unhosted wallet is a non-custodial wallet managed entirely by an individual. This includes cold wallets such as Ledgers, Trezor, and SafePal, as well as hot wallets like MetaMask, Trust Wallet, MEW, and many others. The only crypto wallets allowed will be ones held by exchanges that require all users to complete KYC checks. KYC stands for Know Your Customer and is typically within the centralized finance industry to protect against money laundering.
If you wish to use an unhosted wallet, you must register it with an exchange while revealing your entire identity.
‘Unhosted wallets’ will not be banned from existing within the EU, but you will not be able to interact with an exchange to convert your crypto into fiat or vice versa.