Aeronca Champ pilot reported an NMAC and a wake vortex encounter with a light twin aircraft on arrival into OGD.

Narrative

[I] was on a routine training flight in a ADSB/Transponder negative aircraft. We were traveling southbound along I-15. We tuned into Ogden Tower 5 miles north of the Power Station (VPOPS) and began listening for outbound traffic. At 2 miles north of VPOPS; we contacted Ogden Tower with position and altitude; then requested the Mountain Road Transition southbound. We reported that we do not have a transponder and was cleared through their airspace below 6300 ft. Maintaining 6000 ft. we began a slight left turn eastbound towards the mountain road and was looking for the road. Approximately 2-4 minutes after being cleared towards the mountain road; we observed a [light twin aircraft] pass off our left side; same altitude and less than 100 feet laterally. The aircraft was opposite direction converging. By the time the traffic was sighted; we were already passing; and felt the wake turbulence of the aircraft shake us. Ogden Tower was immediately informed of the near miss; and we were told that as VFR traffic we had see and avoid responsibilities. This did NOT occur inside of Ogden's airspace. After landing; [the] Flight School was contacted and the instructor flying the [light twin] was informed of the near miss; he did not make visual contact with us at all; and he was monitoring Tower frequency as well. There is not much that could have been done to avoid this situation; as we were both in contact with the Tower; and both did not have visual contact with each other until it was too late.