im no expert, but not posted in a while, so thought I woudl use this as an escuse.
RE. Camera in the rain. Last time I had to shoot somethgin in the rain, I modded a loarge clear (tescos) freeezer bag.
camera in the cold, well me in the cold, I modded a pair of leather gloves to keep my pinkies warm (cut a slit in the shutter finger and just pop my finger through when i need to press ) I found shooting with gloves on felt wrong before that mod.
RE. the pic above. I am sure some of the experts are going to have a great idea to fix that. I woudl image the easy way woudl be slower shutter speed so that the raid drops arnt frozen, but that of course wont help much with your chosen subject, because you need a fast shutter to capture the horses without blur.
Software wise, have you tried noise ninja (or similar) on it, not what it is designed for, but a bit of tweaking mihgt help. other than that I think a painstakingly long spot removal and horse reconstruction would help.
I just had a little go at it, and yeah spot removal will do it, but its going ot take a while.
I personal would just do the horse and rider. If you dont like that look, maybe consider doing a slight blur on everything else and create som fake DOF