Access iCloud mail via http from iPhone
You can use a 3rd party browser to access icloud.com without being redirected to https://www.icloud.com/iphone_welcome. But beware, as you will see, icloud.com is not designed for a small display size like the iPhone's.

The key to accessing icloud.com is that the web browser doesn't identify itself as Safari Mobile.

Many browsers I tried, including Opera, Mercury and vBrowse, didn't work. I could finally find one which offered exactly this functionality: the full version of Atomic Web (note: I'm not affiliated with Atomic Web in any way) lets you set the browser identity to Firefox, Internet Explorer or Safari Desktop. 

I chose Firefox 15 and could successfully load icloud.com. However, I soon noticed how uncomfortable it is to browse icloud.com from an iPhone. 

To begin with, I couldn't sign in. I pinched and swiped but the display's contents didn't zoom out nor scroll. This is what I saw:



I had to switch to full screen to be able to partially see the Apple ID field: 



I tapped on the Apple ID field, the metallic iCloud sign-in window gained focus and could log in. 

As I feared, only the left top area of icloud.com's main page was displayed. Luckily, Mail's icon was visible and I could start it:



It was a frustrating experience. I changed orientation several times because, as before, I couldn't reliably scroll. My happiness faded and eventually, tired of trying, I gave up.

I tried Safari Desktop, the WAP browser and IE, but same result (or worse). 

So there is a good reason why icloud.com redirects you to use the iPhone apps: icloud.com is not designed to be used with such a small display. 

If you really need to have access to iCloud's webmail do yourself a favor and consider getting a tablet. If it's an iPad, install something like Atomic Web. If it isn't, you will be able to access it using the device's default browser.