Nothing bad will come of not bathing, unless there is something wrong that causes them to need it. They don't need baths every few months, and frequent bathing with shampoo can actually be detrimental to their skin and coat.
I know someone who doesn't brush her horse's mane at all, and Maggie's got the longest mane I've ever seen on a horse in person. Also, excessive brushing of the mane and particularly the tail can cause it to become very thin and short, as it pulls out the hairs.
Not having a bath won't make them suffer. For the most part horses don't need baths at all. They simply come as a convenience to us humans. Just keep brushing. And brushing, and brushing... And more brushing. Eventually, it'll pay off. Make sure to be very thorough in the process as well. Don't be afraid of applying pressure either, as some horses actually prefer a more vigorous grooming.
All it takes is patience and elbow grease. LOTS of elbow grease. You'll get there :) And if you need any help or tips, the internet is your friend. A very useful friend.