I'll present you what I could find on the subject. It is not an easy subject to research.
Here it is:
First it is an extract from an article released in 1981 by Brig. General Jack Summers and Rene Chartrand. It is the best written reference on the dress that I could find.

Dress

British provincial corps of the American Revolution was supplied with arms and equipment through the established military stores depot in North America and with clothing shipped out from England on contract. However, clothing and equipment were frequently in short supply and units were issued with whatever material was in store at the time, or could be obtained locally. Thus, it is difficult, if not impossible, to be certain of specific details of the dress of any provincial corps at a particular point in time.

Initially, most provincial units were dressed in green coats, lined white, with white waistcoats and breeches. The Queen’s Rangers wore green but the facing colour is not known for certain. Some contemporary evidence shows green facings while other documents mention black collars and cuffs.

In 1778, the British introduced the red coat as a common colour for all regiments, provincial and regular. Simcoe, however, appealed to the authorities for permission to retain the green uniform of the Rangers. He said ‘green is without comparison the best colour for light troops; if put on in the spring by autumn it nearly fades with the leaves preserving its characteristic of being scarcely discernible at a distance.” Simcoe’s request was granted and the Queen’s Rangers retained their green jackets.

In addition to retaining green as the basic colour of their dress, the Rangers developed a distinctive uniform which set them apart from the corps, and helped foster an intense regimental spirit. Simcoe obtained sleeved green waistcoats with green cuffs and fall-down collar and white metal shoulder chains, to be worn as an outer garment during favourable weather. This was worn with white knee breeches and calf-length gaiters or with white gaiter-trousers. A long green coat of standard British Army pattern was worn over the waistcoat as an outer garment in colder weather.

The Rangers adopted a light infantry cap of the regimental pattern for all companies except the grenadier and highland companies. The grenadiers wore a high cylindrical cap of smooth fur. The regimental light infantry cap had a high front, like a low mitre-shaped grenadier cap, of plain black with a crescent device.

Cross belts and pouches were black and all other equipment was of dark colours to keep the Rangers as inconspicuous as possible.

When offered the services of some dragoons to provide cavalry assistance during the Germantown operations, Simcoe was struck by the fact that the dragoons in their red coats and white cross belts were clearly visible at a distance, while his own men were dressed and accoutered for maximum concealment. He felt it would be better to mount a dozen of his own men, rather than employ dragoons. These few men developed into a mounted force of five troops of about forty men each which Simcoe uniformed at his own expense.
The original troop was designated hussars and dressed after this fashion, while the remaining troops were formed and clothed as light dragoons. Simcoe’s hussars wore short green jackets, green trousers and short black boots. A cylindrical hussar pattern cap was adopted when one of the troopers, wearing an American pattern light cavalry helmet was accidentally shot by a jager. Simcoe’s light dragoons wore short green jackets, buckskin breeches, riding boots and light cavalry helmets of the Tarleton pattern. Both hussars and light dragoons wore white metal shoulder chains and belts of black leather. They were armed with swords and pistols only.

There is no clear evidence as to the pattern of headdress worn by Simcoe’s troops of light dragoons. Lefferts quotes invoice for the Queen’s Rangers in 1781 which lists ‘caps with black bear helmet’ and in his work on the uniforms of the American Revolution appears to have interpreted this to mean the Tarleton pattern light dragoon helmet. While this assumption must be considered speculative, it is not unreasonable. Simcoe’s light dragoons were attached to Tarleton’s Legion for a time in the Carolinas and had access to this type of helmet.
Lawson suggests that a horseman in a contemporary painting of the battle of Germantown, wearing a brass cavalry helmet with a red mane on the crest and the front edged with black fur, may be one of Simcoe’s dragoons. A painting William Jarvis of Simcoe’s Legion and his son, done in 1785 shows a black headdress, similar in shape to the rangers’ light infantry cap, edged in black fur. The British supply system being what it was in North America during the Revolution it is possible that all three patterns of headdress were worn at one time or another during the existence of the Queen’s Rangers.

I'll be back with some pictures and illustrations.
Cheers,
Zeno

Here are the first pictures: