Note how a lot of instant kills are designed to be under "suggested plants." This is because they can easily be used against the Zomboni.
Plant Sunflowers and Potato Mines in the beginning of the level to kill the first few zombies and obtain more expensive plants. Start planting Repeaters preferably when the first Conehead Zombie arrives.
When a Zomboni comes, use a Jalapeno to kill it and its ice trail. If you don't have enough sun, plant a Squash to kill the Zomboni. However, it will not take away the ice trail.
If you wait for 30 seconds, the ice trail will go away.