Before deleting your iCloud account, you must save your emails locally because Apple permanently removes all mail data. The easiest way is to
export iCloud emails to Outlook by creating a PST file. Since iCloud doesn’t support direct PST export, you can either sync iCloud Mail with Outlook using IMAP and then export it to PST, or use a dedicated MailConverterTools iCloud Mail export tool that directly saves emails into PST format. Once the PST file opens correctly in Outlook, you can safely delete your iCloud account.