A few weeks ago I was having steering wobble on my red loyale sedan. Tires were my first suspect. I swapped the driver front with back but still had wobble most pronounced going slow.

 

Since I knew I was going to be putting snow tires on in a week, I didn't bother swapping the passenger side. Well the snow tires are on and no wobble.

 

This could have been many other steering and suspension components. The tires actually look new by visual inspection. 

 

Come spring time, I will get a new set.

I have had wobble like that. Gets bigger while slower, fades to near zero on the highway. Found that part of the tread on a front tire was separated from the steel belts. Turned out both front tires had the sam problem. Swapped them for another pair, and a week or so later, same thing. The alignment was too far out. Adjusted it, swapped on another pair, and no problem. The car steered better also.