Getting a DUI on private property is possible. The DUI laws are written that you can be charged with driving under the influence anywhere in the State of Illinois. Therefore, if you drank too much and were using a riding mower or snow machine (snow mobile), it is possible to be charged with driving (your lawn mower / snow machine) under the influence.
However, a Statutory Summary Suspension requires you to be on a public road. Therefore, you should not receive a Statutory Summary Suspension. Although most police officers are not aware of this limitation.