New Hampshire was one of the poorest States (I think only North Carolina, and possibly Georgia, were in a worse condition economically) and uniforms were not plentiful prior to 1778/1779. Thereafter, as part of the New England division of the Continental Army, NH regiments were supposed to have white facings, and are known to have done so even when wearing brown uniforms (actually captured British coats, dyed) in the post-Yorktown stage of the war.
Also, bear in mind that pre-1779 it was common for regiments in many States to have more than one official uniform – initially this was because units were formed from numerous pre-war militia corps, but as the war progressed it was simply the inability to find enough coat and facing material of the right colours to equip an entire regiment/battalion. The NH unit that Lamb's 9th Foot encountered at Fort Ann at the start of the Saratoga campaign had at least two known uniforms, of which one was the light blue coats with red facings shown in the Mollo-McGregor book.
Katcher's "Uniforms of the Continental Army" gives the NH uniforms (all three regiments) as brown coats faced red, with white breeches and waistcoats, and brown overalls. However, this is from November 1778.
Prior to that, as 79thPA suggests, the 1st NH wore green coats, red waistcoats, green breeches, and fully cocked (ie tricorne) hats – this is based on five men who deserted around the same time, so it is possible that one or two companies may have worn all green. In 1777, they appear to have had no common uniform, whilst by 1779, they were wearing "rifle vests" (hunting shirts) and "tow trousers" which I suspect meant overalls.
In 1777, the 2nd NH wore the uniform described above, with red waistcoats and blue overalls. By 1779, the unit was uniformly dressed and the officers at least are thought to have worn the regulation blue coats faced white.
The 3rd NH appears to have been the least well supplied, but even if they were non-uniform before then, they also had the late 1778 brown and red outfit.
All three regiments were combined post-Yorktown, and wore the captured British coats dyed brown (the 1778 brown coats were from France and had slashed cuffs).