In my house the kids can choose the snack they want at snack time. So if I am in the shower at 10:00 am and my 4 year old wants a snack, I say yes, choose something healthy. Then I remind him of the healthy choices we have. So off he goes into the fridge and helps himself to a healthy snack. He's happy, I'm happy . . . and clean.
When my 2 year old wants a snack and goes to the fridge, if it is snack time, no problem, and I will help him make a choice. If it is not snack time, I redirect his attention.
When my 6year old daughter comes home from school I allow her to choose her snack. She is capable of getting it herself. No problem since i am in the kitchen anyway. if she picks something riduiculous, then she needs to change it.
I am one of those people who loves to control everything when it comes to my kids. I am also one of those people who realizes that controlling everything in my children's lives can have serious consequences.
I want them to learn how to make proper food choices. The only way to do that is to give them the space to do it. Of course I am watching closely to lend some motherly advice.
Some times, like today, I have been out of the house for much of the day and unbeknownst to me, my daughter made some very poor food choices, starting with candy from the memorial day parade. She now has a bellyache - what a great teaching moment. So now if I see her making a not so good choice we will talk about ow she felt when she made bad choices in the past.
I know that if I control every single move they make, once they get a taste of some freedom, all hell will break loose. Boy have I seen that happen so many times in college!
I am a SAHM. My job is to teach my kids. When they reach a certain age I will teach them about making proper food choices.
I do not think it is bad that your 3 year old goes in the fridge, but i do think she should ask first. As long as someone helps her make the right choice at the right time, I think it is fine. Setting limits while giving indepenence is a good thing.