Someone once told me there are two kinds of people. Those who pick their nose, and those who lie about it. Now I don't know if that is completely true, but I do know that sometimes there are irritants in a nose, that don't even come out with blowing. And children find that the finger is just the right shape and size to get rid of them. You just need to teach her the right way to get rid of it. It takes time and paitence, and willingness to try different technics.
Think about why you have a problem with your daughter picking her nose. Is it because you think it looks gross? Are you worried about what others may think? So you think it is unhealthy and unsanitary? Anyway think about what your reasons are, and then try to find a way that she will understand to deal with it.
For example, with my daughter, I think it is unsanitary and can make her sick. So I told her that it can make her sick, and then taught her how to use a tissue to clean out her nose, and then told her to ask when she needs a tissue. Now sometimes she still picks her nose, but other times she asks for a tissue. And I praise her the times that she asks. Hopefully she will figure out the right way to take care of her nose over time. By the way my daughter is almost 3. So your daughter may or may not be ready to understand that kind of logic. But think of your situation, and your daughters level of understanding, and you may come up with something.
Merry Christmas!