I've been shooting hockey for several years with a 30D, and now, most recently with a 70-200 2.8 IS II.
(which would be better with a FF, cause it's sometimes too much zoom for the 1.6 crop factor.)
Shooting thru the glass is like shooting thru a big stack of cheap filters- even if the glass is clean, it's going to
dull the image- so I try to get in the penalty box and shoot from there, but I have to duck a lot.
I'm always fighting the metering on the 30D; while the 5DmkIII should be better, the biggest problem I found was when I was shooting the home jerseys, which were navy. So, the meter would be trying to make the ice an 18% gray, or the jerseys an 18% gray; I finally gave up and went to Manual, and set the exposure that way. Also, you might consider a custom white balance- different rinks have different - but always low cost- lights, that have there own color cast.
I'm saving my pennies for the 5D, and hope to see how much better it is, but, maybe there's a couple things to try.