I use GMail as my email client, but iCloud is fine as well. The steps to transfer email from one account to another is almost the same regardless of where you are coming from and where you are going..
Use an email program and setup both the accounts (AOL and iCloud in your case) in that program. You should now download all of the email (with their folders, if you've created any) from the original email account and then copy them all to the new email account.
Before you start removing things from the old account or deleting your account itself, you have to confirm that all the email is correctly there. You can do that by signing into the Web Interface of iCloud.
Now as far as email programs go, if you wish to use Mac Mail as your email client (recommended) with your new iCloud account, I would suggest that you use
Thunderbird as the email program you use to copy the emails around. Once everything is setup the way you want, you can remove the Thunderbird program, as well as, delete your AOL account and emails and use the iCloud account from now on..