As a reminder, the State has laws about operation a snowmobile on roadways ( "highways" are defined as township roads pursuant to Section 2-205 of the Illinois Highway Code.)
In Richmond Township snowmobiles are permitted on the roadway  on West Solon to cross the the bridge, on Pioneer Road to cross the bridge, and to make a direct crossing to the other side of the roadway.*

Operation on Highways. It is unlawful for any person to drive or operate any snowmobile on a highway in this State except as follows:

1. To make a direct crossing provided:
   1. The crossing is made at an angle of approximately 90 degrees to the direction of the highway and at a place where no obstruction prevents a quick and safe crossing; and
   2. The snowmobile is brought to a complete stop before crossing a roadway; and
   3. The operator yields the right of way to all oncoming traffic which constitutes a hazard.
2. Snowmobiles may be operated not less than 10 feet from the roadway and in the same direction as traffic.
3. Snowmobiles may be operated on roadways when it is necessary to cross a bridge or culvert or when it is impracticable to gain immediate access to an area adjacent to a highway where a snowmobile is to be operated. 
   
   * Other locations may exist to safely navigate around culverts or other hazards.
   Full text can be found in the Illinois Compiled Statutes, Chapter 625