If this is your first horse and you do not know things like this, I would more than suggest that you get a book and read up on some things, for example do you know what to do if she accidently gets into a bucket or two of grain and then drinks water?
As far as your question -- it is normal for horses to have runny noses, any or all; the time, especially if it is windy and dusty. What do you feed her? if you are feeding her grain, and it is dusty, you might want to sprinkle a little water on it when you feed her. You might also want to sprikle down where she lives outside, to knock down the dust every day or two. See if the hay is dusty or moldy, but that probobly isn't the trouble. I would not worry about it, but get a book, promise me, and read up on horses and their health problems. Horses do not have the ability to burp or vomit, and if they eat the wrong things, they can bloat up and die from it. Feel free to get in touch with me if you have any other questions, for I have had horses since i was 10 yrs old.