In general there are two times a year to fertilize trees: early to mid-spring and late fall. In spring, nutrients are converted to essential plant compounds that encourage stem, trunk and root growth. In late fall, some nutrients are used in root growth, with the remainder stored in other plant tissues ready to be used when the roots resume absorption and expansion in the spring.
By fertilizing in the fall, some of the nutrients will have a chance to be absorbed by the roots and will already be in the ground when the roots resume functioning in the spring.
Since we don't see the roots, we often don't realize that they continue growing and absorbing nutrients long after the leaves fall and begin work again in the spring before the leaves return. After all, they must be absorbing nutrients and water to enable the leaves to resume growth.
A tree may be getting adequate nutrients from the soil already, but it may benefit from additional fertilizer to keep it growing at its best. A healthy, vigorous tree is much less susceptible to attacks from disease, insects, and other stresses.
So how do you know if your trees need fertilizer? A tree may need fertilizer if: 1) it has little growth, even though it is established and there is adequate rainfall 2) its leaves in midsummer do not have a good green color, but are yellowish 3) its leaves gradually become smaller, year after year 4) its leaves turn to their autumn color and drop in August or early September
Seek the advice of a certified arborist if you are concerned about your tree and whether you should fertilize or not.