I can't find rules for animal handling or mounted combat. Did anyone come across anything? I know horses are rare in the North and often used for carrying goods only but I intend to play a prosperous mounted Barding Messenger seeking out the shadow rumors surrounding the Shire. Also, animal handling in general. I'm missing this particular skill or description within the offered skills. Could be enheartening but there is no mentioning of animals...Any thoughts?
as Asrath mentioned, 1st edition had horse rules so if you can get hold of a 1st Ed of the rohan sourcebook you probably could adapt it relatively easy. Here the getting the book is probably harder than converting any rule specifics.
for generic animal handling checks it basically applies the same skills as you would for a person, persuade, inspire, song etc depending on the specific objective and chosen means.
thematically, I probably wouldn't go too much for actual horse combat in your scenario. My thinking is, that for one in that situation your horse is a very precious resource that your char far from home might not want to risk in combat, in particular with probably low chances of replacing it. Secondly, mounted combat probably works better in an army context with multiple horses in a charge and at least a few bits of armor.
And something to consider from a meta party perspective, mechanically and thematically party combat works better if either all are mounted or none, because mounted combat should happen with the speed of the horse. (not counting stuff to actual mounted combat where an archer sits on his horse in the back stance and shoots - as that is practical foot combat perhaps with an occasional horse handling check)
Not wanting to dissuade you from anything, just a few things that might be worth considering.