No. You will lose Windstream access to your email when you cancel your subscription. To continue your email contacts, use an email client like Gmail to import your contacts. You should also create a new email service, make email forwarding to copy your new Windstream emails to your latest service, and then tell people on your contact list regarding your new Windstream email address.
It's a good thought to do this well Afore of time before cancelling your Windstream subscription. While your Windstream email access may not be cancelled immediately after you send your discontinued notice, you will lose your Windstream email login access shortly after.
Go to the Apple Menu > System Preferences > Internet Accounts and delete the account in question if it shows up in the list. I hope this helps.