What happens to webmail when changing nameserver?

I want to migrate a domain name to my new BH hosting, but the domain has acquired many emails (100s) that I need to reply to. If I change the name servers what happens to the collect mail?

I'm holding off changing name servers till you guys advise as I don't want to loose the valuable webmail

No replies?? C'mon guys

Changing the name servers wont delete whats in a particular mail box. You even will probably still be able to access them all by going to your old hosting's webmail (I do that with a few domains that I no longer have control of).

First POP/IMAP in with thunderbird and download of all the emails to your hard drive. Then you can go ahead and change the nameservers/setup your hosting. Once the the new mail servers are working with the right address, you can just update your tbird account settings with your new information and reply to your old emails.

Hope that makes sense.