It's important to note here a key distinction between British (army) officers and Continental officers.
The former, overwhelmingly, had purchased their commissions into a specific regiment; and were required to purchase their promotions (usually within the regiment) as vacancies occurred which they were eligible for. The latter were, largely if not universally at the lower levels up to Captain, elected by their comrades-in-arms.
The consequence of this difference is that British (army) officers, with only rare exceptions, men-of-means: which is to say gentlemen. A gentlemen was expected to act and dress as one, which included wearing a powdered wig. A Continental officer on the other hand, especially at the lower ranks, was most likely to be a working farmer or small businessman well regarded and popular with his peers. He might don a powdered wig much as we would a tuxedo, for formal occasions, but certainly not every day.
However, there would be exceptions, particularly on the Continental side. The choices made by characters in your WIP are character tells. Let the characters reveal themselves to the reader by their choices.
If it comes up, note that the Royal Navy operated very differently, and relied near completely on merit-based promotion. (However those of means could arrange midshipmen post for sons at a younger age, giving them a leg up to Post Captain provided they passed the Lieutenant's exam.) This is well covered in both the Hornblower and Aubrey novel series.
Finally, to expand slightly on the above which might be unfamiliar to some, my answer to Can the assignment “Depot Battalion” in Hart's Annual Army List be linked to a specific regimental assignment? discusses in more detail the British Army promotion system. Although set a century later, when the system was just being revised to the modern (more) merit based system, it is mostly similar:
Within a specific regiment, commissions were purchased from the Colonel; who in turn had purchased from the Crown the right to be reimbursed the expenses of the regiment in exchange for raising and equipping it. Access to promotions was strictly based upon seniority (unless one was compelled by severe financial distress to decline a promotion opportunity).
Upon reaching the rank of Captain in one's regiment, plus modest service completion, an officer was eligible for secondment, or general assignment, to the army at large. This might be anything from a staff appointment to command of a brigade or larger as a general officer. This is the origin of the military term general.
Military Career of Arthur Wellesley notes that:
Wellesley rose in rank by purchasing his first four commissions, as was common practice in the British Army for wealthy officers.
Wellesley was gazetted ensign on 7 March 1787, in the 73rd (Highland) Regiment of Foot, and became an aide-de-camp in October. He purchased his commission to lieutenant on 25 December 1787, in the 76th Regiment. As a junior officer he transferred to the 41st Regiment soon after to avoid duty in the East Indies, and in June 1789 transferred again, to the 12th (Prince of Wales's) Light Dragoons. He obtained his commission as captain on 30 June 1791, in the 58th (Rutlandshire) Regiment, having served the regulation minimum of three years, and again to major on 30 April 1793, in the 33rd (First Yorkshire West Riding) Regiment, having served six years. He purchased his final commission to lieutenant-colonel on 30 September 1793, at the age of 24. From there on further promotion could only be attained through seniority, per Army Regulations.
Miscellaneous References:
General Regulations and Orders Relative to The Duties in The Field and in Cantonments (1798) - The Marquess Cornwallis
Rules and Regulations for the Formations, Field Exercise, and Movements of His Majesty's Forces (Adjutant General's Office - Montreal, 1793)
General Regulations and Orders For The Army - Adjutant General's Office (1822) [The oldest edition I found.]
