There are a few reasons for this. We use interior white latex paint (lime + water, essentially) and we spray it on. Using a paint brush takes more time.
1. Sun scald, or southwest injury, happens when there are fluctuations in temperatures which cause a tree’s bark to crack. Warm sun absorbed by a dark trunk during the day followed by freezing temperatures at night may cause the bark to split. White paint reflects sunlight that might otherwise be absorbed. Cooler bark during the day leads to less splitting, and less chance for bugs or diseases to enter the trunk.
2. Mice, moles and voles can girdle* a tree under the snow cover. White paint confuses them, as it alters the trunk’s appearance. In addition, it probably doesn’t taste very good.
*What does the word “girdle” mean? It means there has been damage all the way around the trunk of the tree. The bark has been chewed off. That means the flow of nutrients and water to the tree has been interrupted due to the damage. If the tree bark has been removed and the damage extends to the phloem and cambium layers under the bark eventually the tree will die. All the nutrients that keep a tree healthy flow through those layers under the bark.
3. White paint can also offer some protection against tree trunk borers. Several species of borers attack apple trees in New England, especially young trees. Dogwood borers are probably most damaging, but roundheaded apple tree borers, apple bark borers, flat-headed apple tree borers, and leopard moths can also be found. Black stem borers, a tiny bark beetle, has recently been attacking stressed apple trees in New England. (New England Tree Fruit Management Guide)

Painting can be a little messy so we always tell our employees to wear clothes they don’t mind getting a little (or a lot) of paint on. Sometimes when they finish the day, it looks like they got more paint on themselves than on the trees!
You may notice that the larger, older trees are not painted. That’s because their bark is thicker and can usually resist the issues mentioned above.