I would think the ease depends on what the handicap is and how much care the person would require from a partner, if any.
Well, the good news is it isn't insanely impossible. A very good friend of mine from high school was in a car accident that rendered him a paraplegic early New Year's Day 2005. His girlfriend at the time ended up being unfaithful and leaving, but he has since found love online. She moved to help take care of him and now they are engaged and happy as clams. It took awhile, but he found someone who not only fell in love with his personality from what she found online, but flew halfway across the world to be with him. There are people out there who see past disability, you just have to search.
I had a brother who had a stroke and it sure didn't keep the women from hanging around. He never really had a lasting relationship after the stroke, but that wasn't so much because of the disability as it was because he was such a dick.
Well, I think it depends on the disability. For years anytime my GFs found out about mine (TBI), they'd split. Found out that it's over image. One explained to me that if people we hung around found out she's dating "one of 'them' ", she;d never hear the end of it, and she'd be considered desperate. I have had a couple girlfriends over the years since me and my wife split up, but since my last accident, nothing. Havn't dated since 2004.