I kind of disagree with MRT2, somewhat.
Although the Schwalbe tire you mention is not a gravel or mud or sand tire, it will be a little better than the smooth tire you are running -- but it won't be as fast. The minimal tread it has offers more traction in a variety of surfaces, you might encounter. A 35-37mm wide tire will ride considerably better than the tires on there now, but the tradeoff will be less speed.
I run Schwalbe Marathon Supreme 35 and 40mm tires on my Crosstrail, and can usually ride thru anything except soft dry sand. And it has way less tread than the tire you mentioned. I run 35 on the front, and 40 on the rear, for good handling, and better ride/higher capacity..
Schwalbe makes excellent tires for bicycles, and get one of their tubes for it also.
If you find sufficient space, a 35-37mm tire might be beneficial, but still not a real off road tire.
Sometimes, you just have to walk it thru!
Last edited by Wanderer; 05-18-20 at 11:19 AM.