If I went with say a 27x12x12 out back and 27x10x12 up front how much would the bigger tire cut back on the ability to play(i.e. 360's, 180's, and the such)?

The ATV in question will be a manual 05 Eiger.

 

super-sloppy-slick-as-ice-mud and ice, you probably won't notice a difference. On anything else, I personally wouldn't even consider it. It's not the fact of not being able to attempt those types of things, or having the power to pull it off. But, you've got a much more aggressive type tire and they tend to grab and want to throw you or roll you and not just slide around. Even in 2wd my tires (26") grab, I can powerslide in the loose stuff but it takes extreme body english. It's a give and take thing, the bigger the tire gets the less "sporty" your bike is going to feel. It's all in what you want to do. Just my $0.02.

Edit, just wanted to mention that this only applies to doing things like 360's and 180's, you can still "play" w/ the big tires.