I also deleted my outlook app last night lol. Most of my reasoning came from this thread actually! If I set up forwarding on my hotmail account through to my gmail and use Inbox, will that still keep my battery use down? Already using Inbox with my gmail account just now and its awesome!
As for rooting, I might just go ahead and do it tonight when I get in from work. Sounds like its going to help massively in the long run.
Yep, just forward find the setting on your hotmail account in their web interface to forward email to your gmail account.
On gmail, create a filter tag email with your hotmail address as "hotmail" (this is really just for your own benefit, you don't have to do this, just makes it easier to see that it came into the hotmail address).
On gmail tell it that you want an alias to send from, it will then ask you for the email address (the hotmail) one and will then ask you for your smtp login details etc, I think it also sends an email to make sure it's yours.
Set gmail to reply from the address the email was sent to, this means that if a gmail email comes in it will reply using gmails servers and your gmail address, if it's hotmail it'll reply using the hotmail smtp server and the reply address will be the hotmail address.
Now any hotmail mail that hits their server immediately forwards straight to your gmail, so you get push email into gmail.
You might have to remove the Inbox app from your phone after making these changes and reinstall it, so that the hotmail address works properly (it doesn't seem to refresh those kind of changes).
You can then (with the aid of a computer), set up your mail client with both hotmail and gmail IMAP and then drag all your hotmail email into your gmail inbox, and all your sent mail into your sent mail box.
Now, all your old email is in gmail as well, so it's all searchable.