Ask Mr. Smarty Plants

Dormant oil has many good uses in the garden to control pests. It is a highly refined oil that coats insects and insect eggs, and will smother them to death.  But there are many cautions that are necessary to prevent damage to plants, effectively control appropriate pests, and successfully spray the product.  Always use the recommended rates listed on the dormant oil package with the appropriate sprayer. The Aggie Horticulture website at Texas A&M AgriLife Extension has the following cautions to consider about using dormant oil.
It is best to spray before buds begin to swell. If buds of trees and shrubs have begun to swell slightly, go ahead and spray. Although some of the buds may be damaged, the benefits of spraying dormant oil far outweigh the possible repercussions. Do not spray trees which are in full bloom however. Applying a dormant oil spray this late will also serve to cover pruning cuts and can serve as a second attack on stubborn pests which were not killed by an earlier oil application. The closer the application is made to budbreak, the grater the kill.
Spraying of dormant oil should occur on a clear day when the temperatures are expected to remain over 50 degrees F. for at least twenty-four hours. The ideal temperatures for application is between 40 and 70 degrees F. in order to get the oil to spread out over the tree and cover all crooks and crevices. Try to avoid applying dormant oil when severe freezing trends are expected in the 3-4 days following application. The use of a dormant oil mixture will not only kill, but annihilate, annual flowers such as pansies, bluebonnets or snapdragons growing under or near plants to be treated. To insure domestic tranquility, completely cover such tender vegetation before spraying nearby trees and vines with dormant oil.
Dormant oil is most often used on scale insects that affect trees. It is recommended to only use dormant oil for specific pests at the appropriate time of year and not as a general preventative. In many parts of Texas mid-February is the time for dormant oils. The Texas A&M AgriLife Extension Insects in the City website has an article by Loretta Cortez about dormant oils. In it she writes: Dormant season applications of horticultural oil can be an effective tactic to kill scale insects and their eggs during the winter months. But with the rapid onset of warm spring weather, the window of opportunity is relatively small in north Texas and many other parts of the state.
Armored scale like obscure and gloomy scale are especially difficult to treat during the summer months, so the dormant season when leaves are off the trees is an excellent time to treat with a dormant oil. Oils are physical poisons, meaning that they act on pests physically rather than biochemically, like most pesticides.  Oils are able to creep under the waxy, protective scale cover and coat the eggs or bodies of the tiny insects hidden underneath.  The oil coating prevents respiration of the eggs and insect, essentially smothering them. Additional benefits of oils are that they are very safe to apply and have minimal impacts on most beneficial insects.
Oils are useful year round, but most oil labels only allow use of higher rates of application during the winter months.  The higher rates, in combination with the ability to achieve better coverage when leaves are off the trees, make these dormant season applications more effective than summer applications.
The higher, dormant season application rates tend to damage green foliage, especially tender new spring growth.  For this reason, it’s important to not delay your dormant season application too long.  Spring will be arriving soon to all parts of Texas and the south, so the next couple of weeks will be the ideal time to apply dormant oil treatments.