Good question! Burning bush (Euonymus alatus) is native to China, Korea, and Japan and has become invasive in woodlands in the eastern US. Presently, it's importation and sale is prohibited in Massachusetts and New Hampshire and it is listed as invasive in Virginia, Connecticut, Tennessee, and several other states.
Whether or not it will exhibit a similar invasiveness in your area is difficult to tell. If you do plant it, you may need to protect it from winter wind and sun to prevent damage to the plant. Euonymus can suffer from an insect known as scale which can cause a loss of vigor in the portions of the shrub infested. Also, burning bush may suffer from nitrogen deficiency when planted in clay soils or soils of high pH; therefore, proper fertilization will be necessary to insure healthy plants.
Some alternatives that you might consider are:
Barberry (non-native), red or green leaf varieties, attrative berries, drought tolerant.
Cranberry cotoneaster (non-native), glossy foliage, showy fruit, reddish fall color, adapts to alkaline soils, drought tolerant.
Sumac (native), scarlet leaves in fall, tolerates dry, poor soils; drought tolerant.
Buffaloberry (native), silvery foliage, scarlet fruit, drought tolerant.
European cranberry viburnum (non-native), good foliage, white blossoms followed by clusters of red berries, adapts to alkaline soils.
For more information on these shrubs or any others that you may be interested in planting, I reccomend contacting your local county Extension office in Circle at (406) 485-2605.
Good luck and I hope this information is useful to you,