Inquiring minds want to know

Is it rude to ask people about their obvious physical traits?

Can I ask people about how they came to have their crooked noses, glass eyes, limps, smashed fingers, etc?

Or is it only okay to inquire if the physical difference seems to be only a temporary malady, like a cast or crutches or pregnancy or a zit.

I am extremely (EXTREMELY) curious about people, but I rarely ask.
When I do ask, I never ask to be rude or make a person feel bad. I honestly want to know. Come on, it's not like it isn't obvious. Maybe it would put a person at ease to know they are actually being seen and looked at straight on.

There is a very nice gentleman who comes into my work with only one leg. I always want to ask if the cold hurts his stump, or have him tell me his story. But I don't ask. I'm sure I could, he's a very nice person. But I hold back because I don't want to embarrass him if it is a touchy subject.

I consider myself to be a pretty nice person. I like to consider the feelings of others, but does that trait make it harder to get to know people? I don't want to step on toes, or cause someone to be uncomfortable.

I think those bad haircuts, crooked eye-liner, tattoos, painful shuffles, black eyes, scars and missing limbs are unique and it makes me think you must have an awesome story to tell.

So don't be mad if I start asking.