You can access your email from the InMotion servers at any time and from anywhere by accessing the webmail login at yourdomain.com/webmail (replace yourdomain.com with your actual domain name)
If you wish to not use the webmail interface and have your emails forwarded to hotmail/gmail, you can certainly do so by creating a forwarder. To have your email forwarded to a third party provider, simply create a forwarder for each account you want to forward. You can do that from your cpanel account and do not have to log into the webmail (squirrelmail, horde, or roundcube) to do so. Simply log into the cPanel, find the Mail category, and select the Forwarders icon. This also allows you to set up multiple forwarders at once, if needed.
To avoid using an email client, simply use the Gmail or hotmail interface to log in from the web, however you can set one up, if desired. This way the client will check your gmail/hotmail and get all emails sent to those accounts, including your email from your domain. The details on setting the client up to connect to the third party will be on their respective sites.
I was reading through your comment it was very helpful, but I need to configure my web account (email@example.com) to gmail or hotmail/outlook. Is there any way to do this ?
Little weak in English Grammer.