In general, the burbs are very equine friendly. There is a nice equestrian facility at Danada in Wheaton, and there are always horses on the trails at the forest preserves in Dupage County. There are many fine stables and boarding facilities throughout St. Charles, Elburn, Barrington, etc. If you need boarding or training, it can be very expensive in the suburbs - more affordable options are plentiful closer to Dekalb or beyond. I'd Contact Joe Guli at 847-642-1015. He is a wonderful person and really knows the suburbs. He owns a Keller Williams office in Libertyville, IL. Libertyville is surrounded by horse sables and horse friendly communities with excellent access to the city, some of the best schools in the state and ranked as one of the top communities to live in the US.
Need am additional guidance, feel free to call us. We don't sell property in Chicago area, but we do have a business in Libertyville. Best of Luck. Sincerely, Terry/847-367-8773