I'm not entirely sure of the situation, but if you looking for a horse yourself a Bashkir Curly would definitely be the way to go. I have two, and they are a wonderful breed. They also come in straight-haired variety as well, and those are said also be 'hypoallergenic', so to speak. Being a relatively rare breed, they've been crossed with lots of different breeds to create different types. Both of mine are more drafty, but their are also sport horses and miniatures out there.
If you just are riding other people's horses and taking care of regular horses, then their really isn't any easy way. Washing clothes, constant showers, etc. You never know, the medical field is always making new advancements and discoveries, and allergies could be next. But other than that, if you are really looking to get your boyfriend on a horse, maybe seek out a Curly. Curlyhorsecountry.com
is a good resource for locating Curly horses and learning more about them, if you are interested. And for fun, here is a picture of one of my Curly mares adorning her winter curl. Ignore her roundness, as she is pregnant, not fat. ;) Her hair gets almost entirely smooth in the summer, and she looks like a sheep in winter. Curlies come in every color, shape, and size, and the degree of curl varies, as well. Just one of those 'you never know until you try' type situations.
Curly or not, I wish you luck. C: I know a handful of people whose significant other is allergic to horses, it can be a lot of work, but still worth it.