The best timing depends on which species of tree you are planting and  where you live.

Deciduous trees.

In a moderate climate like the New York Metropolitan area,  deciduous trees can be planted in late spring or early fall, although fall is usually regarded as the best time. Six to eight weeks of time should be allowed in the ground before the expected stress of extreme cold or heat. The tree will then have a chance to develop some new roots before winter or high summer comes. There is, however, some evidence that trees with fleshy root systems, such as magnolia, tulip tree (Liriodendron) and yellowwood (Cledastris kentukea), are more successfully planted in the spring.

In colder areas (zones 1 - 3), early spring, when the ground has thawed, is the best time. If they are planted in the fall, then they will not have time to get established before the extreme winter conditions arrive. In warmer locations (zones 9 - 10), fall is also the best time to plant. The trees will grow slowly throughout the winter and will be well established before the hot summer.  

These rules apply mainly to large ball and burlap trees. With smaller, container-grown plants you have more leeway; they could be planted in summer if they are well watered throughout the hot months. Even so, fall is still the best time in the northeast even for container-grown plants. Deciduous trees purchased as bare root plants are sold in dormancy and should be planted when the soil is unfrozen in late fall or early spring.

Evergreen trees

The same rules apply to evergreen trees as deciduous trees. One difference, though is that evergreen trees should be planted a bit earlier in the fall. About 4  - 6 weeks before the expected first frost is a good guide to allow roots to develop . These plants will need to nourish themselves throughout the winter as they continue to bear leaves and photosynthesize.  Hemlocks, however, are best planted in late spring. Broad-leaved evergreens (mainly shrubs) should be planted in the spring.

Courtesy of NYBG Plant Information Service

References

 J. R. Hartman,  T. P. Pirone, and. M. A. Sall,. Pirone's Tree Maintenance. pp. 75-77. 7th Ed. Oxford University Press. Oxford. (2000).

G. W; Watson and E. B. Himlick, The Practical Science of Planting Trees. pp.  55 - 65.  International Society of Arboriculture. Champaign. (2013).