Was it cancerous? Was it gunk? It was quite hard the first time I poked at it, and when I googled it, I found that it can actually be dislodged if I do it carefully with a pointed object, like the pointy bit of a chicken feather (tons of those lying around on the ground at the moment). It turned out I didn't need to do, that I started doing it with my fingernail and it did start to move and I could move it out. It came out like solid cheesy gunk, much like squeezing a zit or a boil, I suppose!
Here is a picture of what someone else managed to get out.
Her nostril afterwards was dilated, and I was worried that she would get more crap into it. She probably will and I'll be picking at her nose again. But at least this time, I know how to do it!
So my suggestion is to get a good grip on your chicken. One site said to tie up her legs so that she can't kick and flap around - I didn't do that. I had her wedged between my legs, so she couldn't back out (I was squatting) and my left hand firmly around her neck, with my right hand picking at her nostril. She would often flick her head away from me but it took time and patience. If your chicken is particularly cantankerous, I think that a bandage wrap around the chicken would work well (like a crepe bandage) or at least a towel to keep her firmly wrapped so she can't escape.
Why does this happen? Apparently feed can get caught in the nostrils, and Snowy with her twisted toes might be more at risk of stuff getting caught in there since she can't scratch it out well. It wasn't anything cancerous, thank goodness, nor was it a canker sore that I have seen in other pictures (yuk!).