Question

What happens to kinetic energy of a snowball as it rolls across the lawn and gains mass

Answer 1

Before we start thinking about the snowball, we need to remind
each other that energy is "conserved".  That means that if you
ever see energy decrease in one place, then the missing amount
must have gone somewhere, and if you ever see energy increase
in one place, then the energy that appeared must have come from
somewhere.  Energy does not magically appear or disappear. 

So you toss a snowball out of your hand.  As you let it go, you give
it some kinetic energy, and it starts rolling along the ground.

Once you let go of it, it can't get any more energy (unless it has
some kind of little tiny engine inside it).

     Kinetic Energy = (1/2) (mass) (speed)² .

and that amount can't change.

So if extra snow sticks to it as it merrily rolls along, and its mass
increases, then it must slow down.