There are a few different ways to handle that. I currently have a gmail address set up on both my iPhone and my iPad, as well as the .me account for my iCloud account. Both accounts show up on my iPad, iPhone, and on my Mac (were I stopped using the web site for gmail and now just use Mac Mail on my Mac). Since I have chosen to just have my msn account on forward to gmail, not my gmail on forward to my .me account, the .me account just sits there. Therefore since I am using gmail, a record of the email stays on the gmail account so I can always retrieve it from gmail either from the site or within the mail program. When I delete an email on the iPhone, iPad, or Mac, it is removed from my inbox on all devices, but a record of that email remains on the all mail box of gmail.
Another way to set it up is to actually use iCloud mail and do the same thing with your other accounts that I did with gmail. If you get the article that I have quoted bellow you will see that you can also set up iCloud mail to either respond or send mail that seems to be coming from your regular accounts and your .me account.
Here is a quote and some directions from the Jan. / Feb 2012 issue of iPhone Life, article on iCloud
To use these features, you’ll need to enable them in Settings>iCloud. Note that in order to use iCloud for email, you’ll need to use an email address in the me.com domain name.
You’ll have to either use this email address from now on, or simply turn on auto forwarding of your regular email account so that everything goes to me.com. You’ll still be able to do your email in the usual way, and you can set it up so that recipients of your email will see your usual email address, not your me.com address.
You can actually use any email client to access your iCloud email.
The settings are:
Incoming mail: smtp.mail.me.com
Username: your Apple ID
Password: your Apple password
Port: 993
Outgoing mail server: smtp.mail.me.com
SMTP port for outgoing mail: 587
Sent from my iPhone/iPad using iPF