driving on ice?

Recently my 1988 golf started handling as though its driving on ice, it feels very light on the steering(not power steering) as I accelerate and feels as though its wandering about at high speed.
I have checked the usual ball joints, steering gear etc but found no problems, even changed front wheels with rear wheels.
All I found was badly leaking rear shock absorbers.
Could the shocks be causimg this feeling of instability?

Yes.