Hobbitmum, There is a good set of links to potted histories for the Greys (and just about every other British regiment - plus many others) at

http://www.regiments.org/milhist/regtintro/index.htm

and a good lightweight description for the Greys at

http://www.btinternet.com/~james.mckay/rsg.htm

The Greys were in Europe a fair bit before the Napoleonic Wars, and during it, and they have the Battle Honours to prove it. They were certainly at Minden and Warburg before the Napoleonic Wars, and also at Willems in the Flanders campaign in 1794.

However, as the Walrus says, they could never be described as "Light Horsemen".

The lists for British Cavalry at 1800 include the following, so you pays your money and you takes your choice. You would have to check all of these out to see who was where and when.... Rather you than me. However,

http://www.regiments.org/milhist/uk/lists/ba1800.htm

will give the links to find battle Honours and histories. One of them might be the one!...

Household Cavalry

1st Regiment of Life Guards   
2nd Regiment of Life Guards   
Royal Horse Guards Blues   

Cavalry

1st (The King's) Dragoon Guards   
2nd (The Queen's) Regiment of Dragoon Guards   
3rd (The Prince of Wales's) Dragoon Guards   
4th (Royal Irish) Dragoon Guards redes 1788 from 1st Horse
5th Regiment of Dragoon Guards   redes 1788 from 2nd Horse
6th Regiment of Dragoon Guards   redes 1788 from 3rd Horse
7th (The Princess Royal's) Dragoon Guards   redes 1788 from 4th Horse
   
1st (Royal) Regiment of Dragoons   
2nd (Royal North British) Regiment of Dragoons   
3rd (King's Own) Regiment of Dragoons   
4th (Queen's Own) Regiment of Dragoons   
[5th Dragoons]   vacant
6th (Inniskilling) Dragoons   
7th (or Queen's Own) Regiment of (Light) Dragoons   
8th (The King's Royal Irish) Regiment of (Light) Dragoons   
9th Regiment of (Light) Dragoons   
10th (Prince of Wales's Own Royal) Regiment of (Light) Dragoons   
11th Regiment of (Light) Dragoons   
12th (The Prince of Wales's) Regiment of (Light) Dragoons   
13th Regiment of (Light) Dragoons   
14th (The Duchess of York's Own) Regiment of (Light) Dragoons subtitle added 1798
15th (The King's) Regiment of (Light) Dragoons   
16th (or The Queen's Own) Regiment of (Light) Dragoons   
17th Regiment of (Light) Dragoons   
18th Regiment of (Light) Dragoons    1821
19th Regiment of (Light) Dragoons    1821
20th (or Jamaica) Regiment of (Light) Dragoons 1792 1818
21st Regiment of (Light) Dragoons 1794 1820
22nd Regiment of (Light) Dragoons 1794 1802
23rd Regiment of (Light) Dragoons 1794 1802
24th Regiment of (Light) Dragoons 1794 1802
25th Regiment of (Light) Dragoons 1794 renumb 22nd1802 1820
26th Regiment of (Light) Dragoons 1794 renumb 23rd1802 1819
27th Regiment of (Light) Dragoons 1794 renumb 24th1802 1819
28th Regiment of (Light) Dragoons 1795 1802
29th Regiment of (Light) Dragoons