The reason for watching her food intake is most likely because Juvenile Diabetes is on the rise, and even if she's eating healthy foods, if she isn't getting enough exercise to burn off the calories, it could be harmful.
My kids would snack all day if I let them; my son (4 yrs) is very picky (but loves fruit and yogurt) where as my daughter who turns 3 in just over a month, will eat just about anything and at times, has out eaten her father! My son once went through an entire bunch of bananas (7) within three hours. Getting that much fruit can be just as harmful as not getting enough. His doctor said that too many bananas (and other fruits) can cause constipation which could cause major problems in kids because if it hurts, they stop going and a trip to the ER is necessary.
They go to daycare two days a week while I am in classes and they get a structured food schedule and I've implemented something similar at home.
When they're home, breakfast is from when they wake up until 8:30, then, I take any uneaten food (or food they've played with) away; if it's something like cereal, I dump it; if it's something like toast, I put it in a ziplock and heat it up later if they want it. Then they play and do not get a snack until about 10:30, usually a piece of fruit or yogurt with granola (Whole Foods has some great granola in the bulk food isle). Then lunch is at 12:30 and it's usually Peanut butter sandwiches with another piece of fruit (but each time they're given fruit, it's something different) I buy the DOLE fruit cups to put in their lunches; they have apples, pears, peaches, mixed fruit and even fruit in a jello like substance (which I don't buy) And every once in awhile, I give them an Oreo or some other treat.
The big key though is getting your daughter moving around more so that she has an alternative to non-stop eating. If taking her outside to play isn't possible, (I can't take mine out to play because our neighbors don't clean up after their dogs like they're supposed to) then see if there is a children's museum. I have a family membership to the Hands on Museum in Ann Arbor so it's free for us to get in. Another idea is to find a public swimming pool and enroll in swimming classes, it's a great way to burn up energy and introduce her to deeper water than her bathtub. Good luck!