Student Pilot reported while landing in a crosswind they lost control of the aircraft and exited the runway into the grass.

Narrative

Pattern work for landing practice. On second landing; touched down slightly right of center line. Plane continued to the right and exited runway into the grass. Plane potentially struck ground objects while off runway. Wind was variable at time of incident based on ASOS report and windsock observations. Left crosswind was present and crosswind correction applied. I observed the nose drift to the right just before touchdown and applied left rudder or reduction of right rudder to correct. Do not recall aileron adjustments; but track of plane after landing potentially indicates that I also neutralized ailerons resulting in decreased wind correction and additional drift to the right. In retrospect; neutralizing ailerons from left-banked wind correction may have also resulted in the nose drift to the right. Upon touchdown; I attempted to steer the plane back to the middle of the runway but did not apply enough rudder to recover. Once plane entered grass I focused on obstacle avoidance and bringing plane to a stop as quickly as possible.