As John said, you need to meter correctly , but in this situation is is probably very hard to do that and get the children playing in shots that you want as keepers. You really need to meter the snow and trying to do that in Automatic mode, just isn't really possible. You need to be in manual mode.

What I did, was did a curves adjustment, picked the highlight picker and clicked on the snow. I then did a little minor adjustment to colour to bring out the red a little more, added a little to the contrast and then saved it for the web, I was trying to show you this as I was typing as well.

I use Photoshop which has quite a few more features than elements does, at one time Adobe was allowing those using Elements to upgrade to Photoshop at a reasonable price, might be worth checking out for the extra new features that it does have, like shadown/highlights adjustments.

I don't have Elements installed on my computer so can't really talk you through it more than I have done above.

Hope that helps.

What camera are you using by the way.