I'm currently building a food forest that I plan to gate in to protect animals. What type/breed of animals should I look into for keeping the forest floor clean?
Many kinds of animals can be used, but chickens are most often selected to patrol the floor of a food forest. I used to allow my hens to have full run of the yard all the time, but they were way too destructive. Now I just let them out for an hour or two when I'm there to supervise. I encourage many kinds of sprawling plants like day flowers, gogi berries, grape vines, blackberries, beans, and various cucurbit crops to penetrate into their permanent area, and they manage to keep that well trimmed, but they get plenty to eat and they don't need to be chomping down everything I want to put into my salad.
At another location I have a much larger food forest area with a wide variety of plants and trees densely packed together. I just allow the deer and rabbits to have free reign of that and they do some fabulous trimming for me. I thought about bringing in a few hens, but they prevent the natural reseeding of the lettuce, onions, broccoli, mustard and other brassicas by scratching around too much before the seedlings can get established.
Keep in mind that a healthy food forest will have a lot of different things growing on the lower levels and on the ground where you want to walk. You can clear pathways if it gets too dense, but it sounds like you just want to have trees and keep the lower levels cleared. This is not the generally accepted definition of a "food forest" but if that's what you want then rabbits, chickens and ducks might all work well for you.
If you have a large space and your trees are tall enough, you might consider getting a few goats. They are famous for keeping stuff cleared, but you can't have just one. Goats and most other foragers are not happy if they are alone. I've found alpacas to be better than goats because they are more gentle with the way they browse and they are much easier to keep contained. Goats are expert escape artists, but they produce fine milk, so the extra effort and expense on the fence might be worth it if you are willing to milk them every day. Alpacas produce a valuable fleece and hens will keep you in eggs, so balance the possible fringe benefits when you weigh your decisions. If you like to eat meat and you don't have a lot of space, then rabbits might be the right answer for you.
A lot will depend on what kind of plants you want to have growing in your food forest. Keep this in mind when ordering. Rare plants growing around animals that like to eat plants can be a recipe for disaster. They might eat what you don't want them to eat, or they might eat what is not good for them. Either way you will be crying unless you research the toxicity of the plants and the tolerance of the animals. This kind of information is a lot harder to find with rare plants that may have never been tested against various types of animals.
It should be much easier to find the information you need when it's time to select the particular breeds. You'll want to select those that hold up well in cold weather. Zone 4a is pretty chilly. For chickens, the Australorp, Cochin, and Silkies are good choices. Rhode Island Reds, Plymouth Rocks, and Barred Rocks are also okay in the cold, but you will still want to build a coop for them. In the winter you'll have to make sure their water isn't frozen over. Ask yourself if you are willing to get up every morning in the dead of Winter to feed and water your babies. If not, then you might just be better off with a weed whacker or a scythe.
Regardless of what you decide, I strongly suggest that you reconsider the whole idea of keeping the forest floor cleared out. A healthy and productive food forest has a wide diversity of plant types that fill every niche. Clearing out the lower levels would be like chopping off your feet. It hurts. If you don't want a wide variety of herbs, vegetables, berries, seeds, vines, shrubs and grasses growing along with your trees, then you might want to research Silvopastoral systems, orchards, or agroforestry, because it might be possible that the term "food forest" does not exactly describe what you had in mind. Better yet, watch this video at https://www.youtube.com/watch?v=hCJfSYZqZ0Y and see if that helps, inspires or informs.