Young trees seem particularly prone to frost cracks but they can occur on trees of any age. There is nothing you can do about it but wait. When the weather warms, the crack will close, often within several hours after it splits. In fact, many cracks may go unnoticed. Extreme cold usually does not kill lawngrass, but it can if there are some contributing factors.
Young plants are more sensitive to cold than mature grass plants.
So a lawn that was just seeded last fall is more prone to problems than an established lawn. If the fall in temperature to -40 F is slow, plants will have time to acclimate and will suffer less damage. Cold often kills by dessication. And because groundwater is frozen, water lost through the leaves cannot easily or rapidly be replaced. If there is no snow cover for insulation, and the wind is blowing, the grass plants simply freeze-dry to death.