It's your choice which email address to use. Apple did not change your email address. They just gave you an additional one you can choose to use, or not use, as you wish.
The "smtp.me.com" mail server is the old, now discontinued, MobileMe mail server. You need to update the mail server settings as per this support article:
Thanks but I am afraid I am no further ahead. I should have mentioned that I had already configured my Mail account on my MacBook Pro when I moved to iCloud with my new iMac and I also didn't emphasise that all seemed to function well for ~3 months. However, I took your advice and did it all again but with the same outcome, message "Cannot send message using the server smtp.me.com The sender address ****.*****@mac.com was rejected by the server smtp.me.com. This brings me to the point you make that the "smtp.me.com is old and discontinued whereas the article on configuring Os X v10.6 gives this as the server to use for outgoing mail. Is this incorrect and the root of my problem?
Thanks for your help
The "trick" is to watch which "signature" you are using, and which mailserver that "account" is linked to.
This has never been clear in any Apple documentation, which is poor at best, and anything but inituitive.
And the article mentioned above it is badly out of date (despite a revision date of July 2012).
It is simply WRONG.
"For the Outgoing Mail Server, enter: smtp.me.com." is NOT correct. In my case, my Icloud server lists itself as "iCloud (iCloud)"
What happens is that when you reply to a message, it will adopt the signature associated with the incoming address. @me.com for example, and use whatever you have configured as THAT account's outgoing mail server.
If in your account setup, you have NOT defined your Me.com "account" to use "icloud.com" as its smtp server, it will attempt to continue to use "smtp.me.com"
Of course there is always the possibilty that Apple has broken their mail handling facility -- again.
You need to set Mail up on Snow Leopard with the correct settings for iCloud: since the 'Wizard' will try to force you into MobileMe settings because it's never heard of iCloud you should follow the instructions here:
Once done you should have no problems with iCloud email - I have it working perfectly well in Snow Leopard.
Thanks to both you & William for very helpful advice. Following on from my initial response to Julian I decided that the article on configuring Mail for OS X v 10 had to be giving incorrect advice. So I did what you suggested and deleted all the existing accounts and started afresh following the article BUT substituting icloud.com for mac.com (I am an original macmail user!) in my e-mail address. Bingo, everything now works! It is not exactly the procedure that you describe, which I am sure is absolutely on the ball but I am loath not to let sleeping dogs lie! If I run into problems again I will keep your advice and follow it next time. The only 'problem' that I have is that e-mails from my MacBook Pro rather than my iMac show the adress of the sender as @icloud.com rather than the address I am known by, @mac.com. However, this is covered by my 'suggestion' in my original posting and whilst I am on that subject I am afraid I would have to disagree with Julian. When @mac became @me the adress on my e-mails was changed, presumably by default by Apple and I received a number of requests to confirm 'my change of address'. i realised that I now had to check the scrolldown but to cover my forgetting to do that I added the note to my signature. My advice was for those who I suspect are the majority of Mail users who are not always so stringent in checking such things. Thanks again to both of you.
After reading your article carefully (excellent!) I decided to avoid any further problems & clean my Mail up and follow your procedure exactly. It works perfectly. I also followed your option with regard to the addresses and of course that gives me the option of which address to use with the scroll down feature as long as I remember to check it! To cover memory lapses I will still stick with my signature message but thank you again for putting me on the straight & narrow.