Well, I can't speak from experience using Arnica for hair loss, but I am studying homeopathy in school so perhaps I can be of some assistance here.
My understanding of homeopathy is that it doesn't just treat a particular disease or condition (i.e. Hair loss) but it treats the entire symptom picture of how one individual experiences that condition. So let's say one person experienced hair loss by suddenly losing big chunks of hair at a time, and another person had a gradual shedding that has thinned their hair over many years. Arnica taken homeopathically might work for one person's symptom set, but not the other's. They might need an entirely different remedy.
I haven't heard of using Arnica topically for hair loss... but homeopathic remedies aren't very expensive, so it probably wouldn't hurt to try it and see if it works for you. In my opinion, though, you'd probably be better off putting your money towards a good multivitamin/mineral, essential fatty acids, biotin, or sulphur supplements (MSM).
Best wishes for healthy growing!