Late fall is one of the best times to plant or transplant most kinds of deciduous trees, those that lose their leaves. Days are cooler and, since the trees have no foliage, they need less water. Small ones can be transplanted bare-root.
One thing particularly to guard against is planting them too deep. Even an inch or two too deep may have serious consequences. If a rather deep hole is dug and organic matter added to improve the soil, the tree should be planted an inch or two higher than it was growing before. That will take care of settling when the organic matter decays.
Trees planted in the fall should be mulched and have their trunks warpped with burlap or tree-wrapping paper, which you can get at large garden centers.
Mulching will keep the soil in the root zone warm enough for root growth to continue for several weeks after freezing weather occurs. The tree will have a better root system in the spring to supply it with moisture.
In the spring, the mulch should be removed early to let the soil warm up sooner. Whereas the mulch keeps warm soil warm longer in the fall, it also keeps cold soil cold longer in the spring.
A four-inch mulch of pine bark, wood chips, sawdust or partially decomposed leaves, held down by chicken wire, is recommended. The mulch also will conserve moisture and keep the soil surface from crusting, which makes it harder for water to percolate into the soil.
After the soil warms up in the spring, the mulch should be applied again.
Protection of trunks by wrapping is particularly recommended for thin-bark trees. Wrapping retards loss of water and subsequent drying of bark, protects the trunk against sunscald and is a partial protection against borers. The wrapping should be left on for two years unless it rots and becomes unsightly.
It often takes two, three or even four years for a tree to become well established in a new location. During that time, it should be watered weekly during prolonged dry weather. It can make a big difference. Otherwise the tree may stand still, making little or no new growth. Another thing to guard against is overfertilization. A little bit goes a long way for a newly planted tree.