I love to hike, and Breezy provided many places to do this. With wintertime, my family used snowshoes and we did much hiking around the golf course as well as taking trips to nearby forests for snoeshoeing and hiking. Just a short distance from Breezy is an old firetower. It is a moderately difficult uphill hike to get to the bottom of the firetower and then many steps to the top, but the view is worth it. This is a great way to expend some of the energy of your kids and get some exercise in for yourself. The route back is quite easy, except for a moderately steep hill to climb down--just be careful with your footing on a snowy, slick slope.
Cranberry Bog Path is a great hiking/snowshoe path near Crosslake, MN, right by Breezy Point. This 4-mile (or so) hike was very easy and extremely serene and peaceful.
Golf courses always provide a great place to snowshoe and the fairways at Breezy are no exception. The traditional course is just off the back of the unit we stayed at, and we were able to follow many of the other fairways on our walks with the kids.