Have anyone experience a wobble in the steering of a 2004 Alero.?

When I attempt to move it right or left it feels like play or a wobble effect at very slow speed like 5 to 10mph.I didn't notice this until I replaced the winter tires with the summer tires.First I thought there might be play in the steering rack.Would a broken belt give you this indication one mechanic tells me it feels like the strut bearings.I had them replaced before but not with this kind of symptom.Do you think it might be a belt since it was nor there until I replaced the winter tires with the summer low profile tires.I thought where the summer tires where a little wider than the winter tires that there was more friction on the road and was making it feel like play in the steering rack.