A wide tire is going to track in the 'ruts' more than a narrow tire. Do you feel slop in the wheel? The gear box could be in need of adjustment. Also all steering linkage should be checked for excessive ware as stated in previous posts. Anti-sway bar end links are another thing to check on. Worn or loose end links will give you a control problem when cornering. Bad shocks will give you bouncing/hopping.
With your description, I'm leaning to worn linkage or gear adjustment. It could also be what I experienced last summer. Look for broken mounting points on the steering gear.