We don't currently own a dog, but sometimes we dog sit and therefore, we've been to some of the area's dog parks and have a few favorites.
Katherine Kearney Carpenter park is actually in Mequon, but it's close enough that you should give it a try. It is our favorite because dogs can be off leash and there are some water features and trails that make it interesting for humans too. There's a large grassy area where you can throw a ball, and get drinks for your mutt. If you want a drink, you still need to bring it with you. Volunteers have been gracious to provide water and plastic poop bags, so even if you aren't prepared, you can still go. This above link gives you a map to help you find the 2 parking lots so you can choose one and enjoy the 35 acres of outdoor fun. I always feel like I get enough exercise here, and the trails are good enough, that I've even taken a stroller. The problem we always have with a lab, is that you can't keep them out of the water. If you have a dog like this, be sure to bring a towel and blanket. The car is always a huge mess after we've been here.
Milwaukee has a website that lists all of their dog parks/exercise areas.
Estabrook park has a fenced dog area but it is not a favorite. It tends to be muddy and is basically an area to throw a ball and clean up poop. Plus you need a permit which you can buy on the spot. They call it an exercise area rather than a 'park'. That part of the park is very near the ponds that contain large numbers of geese and ducks, so it's important to keep your dog on a leash while you are going from the car to the exercise area. There's a similar exercise area in South Milwaukee on Lake Drive at Warnimont Park. Both areas actually require a permit.
Granville Dog Park was the first off leash dog park that I know of. It's nice but will be getting some updates. There was a meeting in early December to talk about the plans, but if you keep your eye on the Milwaukee Dog Park Link, you can learn more. This is an excellent blog about all the dog parks in Milwaukee county.
Now you have some excellent links and information about where to go with your doggie pals. Snow or shine, they still love the outdoors!