Certainly some were, but probably some (most?) weren't uniformly dressed. Unfortunately very little evidence survives. I'd certainly expect dragoon regiments of the main field armies (Oxford, Essex, Waller, Manchester) to have received uniform coats, but little or no information is available.
Okey's definitely got red coats as part of the NMA
Royalist dragoons of the Oxford Army probably received the 1643 clothing issue so likely were either redcoats or bluecoats (and might have got the full set of matching montero hat, coat and breeches).
I've heard it said that for the Royalists, Corbett's Shropshire regiment had green coats, Washington's (ex-Ussher's, sometimes known as Prince Maurice's) had light blue coats and Sir Thomas Hooper's (ex-John Innes, sometimes known as Prince Rupert's) had red coats. However I've not seen any clear evidence for any of these so don't trust them!
Some other Royalists with vague snippets/suppositions
Earl of Crawford's Dragoons – possibly redcoats (scribbled note!)
Sir Edward Duncombe's Dragoons – possibly redcoats (Stuart Reid O&R)
Earl of Northampton's Dragoons – redcoats (O&R)
I wouldn't bet more than a fiver on any of the above except Okey's. Would be great to hear if anyone can confirm or deny the above and say if there are any other leads!