Your e-mail is your only lifeline to facebook and it is used by Facebook to identify you with your account. If you do not want to risk losing your Facebook account and get trouble whit your Facebook login, you must have a working e-mail address registered on your account.
Regardless of where you obtain your e-mail address it's always a risk that you will lose it sooner or later. You may be out of a job if you have a work address. You might move if you have your email account with your landlord. You may forget the password to your hotmail account and get rid of it .. Your free e-mailprovider may face bankruptcy, you finishes school and so on.
You will very likely at some point change your email address, and sometimes you loose control over it. If you forget your password you can't get a new one and you will not be able to login on Facebook.
Would you get rid of your e-mail address, you can of course get by for a while you can still log in with it. But if you forget your password and need to renew it so you can no longer get such because you do not get the message that Facebook sends out. Would there be any control from Facebook requiring response by e-mail, you can not respond. Does your account hacked so someone replace your password as it is also driven. In addition, you also no notifications about new friends, etc..
If you know that you are changing e-mail address is of course easy to change the address in your settings on Facebook before you changed. But it is easy to forget. My advice is that you can now register an email address. Register on any sites that offer free email addresses such as google or hotmail. Feel free at any of the larger more well-known places, so you know they are there, even though a few years.
Then be sure to put even the address on your account with Facebook. To do this:
Log into Facebook
Now you have an email address that you can use if you lose your old one.
Remember to save your login information for your new
e-mail account (ie the ones that you received when you bought it on hotmail, google or wherever you did it). Since the new e-mail address only to spare, you may not need to use it for several years. Then it is that you remember where credentials are ..
It can also be useful if you are using the test sometimes. Some free services deletes email accounts that are not used automatically after a certain period of time ..