a friend of mine had the same problem with her 3 yr old, so we tackled it together (i was her live-in mommy helper, daddy was in iraq).
when he woke up that day, we sat him down and said that picking is rude, no one wants to watch it, and you should go to the bathroom and blow. we told him if something is stuck in there, pick it in the bathroom alone, wipe it on the tissue, and wash your hands. the first time we saw him do it in the morning, we would warn him- 'the next time you pick your nose in here without a tissue, we will put socks on your hands'. he did, we put them on, took him to the bathroom and helped him blow. after he wore socks for about an hour, we took them off. the next time, warned him again, then brought out the socks. after about a week, he was in the bathroom with a tissue, blowing, not picking.
anyone caring for her needs to know what you are doing, so that they may reinforce.
good luck!!