Answer: Generally speaking you could plant container grown plants that have been stored outside and are still dormant, assuming the soil is workable. This would mean not too muddy or frozen, for example. And, the plants should not be in active growth with swelling buds or already leafed out. If they are already leafed out or beginning to leaf out, you would need a cool greenhouse to keep them in until the weather settles and freezing weather has fully passed. Dogwood trees are often a bit difficult to transplant due to their shallow root system so you need to reduce stress as much as possible. If they have already begun to grow, frost --let alone freezing weather and sharp temperature oscillations -- would damage the tender new growth and could severely shock or kill them.
If they are wrapped in plastic, I am not sure what stage of growth they would be in. For this reason I would suggest you consult with your local professionally trained and certified nurseryman prior to purchasing. Also verify whether or not there is a warranty on them.
I would not recommend Cornus florida (our native dogwood) for a full sun location especially in your area with its hot summers. They would be suited for a location with gentle morning-only sun or bright dappled light all day. In nature, they are an understory or edge of the woods tree. Dogwoods also require an evenly moist yet well drained soil that is acidic and high in humus or organic matter. They are shallow rooted and will not do well in a hot sunny or dry location. They also do not make a very good shade tree because they have a horizontal growth pattern with very low branches (these shade the root area to help keep the soil cooler and moister naturally) so it is difficult to walk beneath them. However, Cornus kousa might be a possible choice as it is more sun tolerant. It also has a more upright form than the C.florida.
The Cotinus on the other hand is very resiliant and able to grow in many different conditions from full sun to part shade, and in any well drained soil. If you need to train it to a tree form, consider a multi-stemmed trunk for a small tree. This will accommodate its natural form with a bit less drastic pruning. The time to prune Cotinus is late winter to early spring before new growth begins.
As far as which tree to plant, you might consider using a larger cultivar of crape myrtle and allow it to reach its full mature size. These will do fine in a full sun location and in tree form can create a lovely shaded area for a patio for example.
Please understand it is difficult to make specific suggestions long distance without a detailed understanding of the planting site -- soil type, soil moisture, sun exposure, wind exposure, the overall space available, and so on along with your overall design goals and preferences. Your local professional nursery staff and/or county extension should be able to help you analyze the growing conditions where you want to plant your trees and identify trees that are most likely to thrive there, then you would select your favorite from those.
Good luck with your planting!
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