Because it's a tiny, focused, hot flame.
What you want is a large, wide flame - nowhere near as hot but hot enough.
There are weed-burners that would do the trick for ice, even little hand-held ones that you can just stick a butane canister on. They work quite well for weeds (they tend to die before they can spread seed, it kills the seed too, and they tend to stay-dead for a while after), and can be handy for a quick de-ice.
Saying that, some pillock will use them underneath their car fuel tank or something, won't they?
But if the field is wet... the field is wet. Leave it alone. Anything you do to it will just damage it more and make it worse to play on.
Go get muddy instead, it won't hurt you.