Do what you need to do first like planting Sunflowers. Delay the first few zombies via the Chili Bean and other methods.
Now plant two Bloomerangs in the minecarts while waiting for Winter Melons to recharge. Plant Wall-nuts to protect you from Zombie Chickens. These two plants will also be a good combo against Zombie Chickens.
When you have enough sun, try replacing Sunflowers with Winter Melons. Continue use Chili Beans if necessary.
Keep planting Winter Melons as your main attack, including replacing the Bloomerangs in minecarts with them. Don't forget to build your defense either, plant more Wall-nuts and when one is eaten, replace by an another one.
Don't forget to utillize the given Plant Food. Considering using it on Winter Melon to deal a huge amount of damage to multiple zombies, as well as slowing them down.