All the ones we used there last year were the basic wooden ones with the rail all around and the strap that buckles at the waist. I never saw any of the reclining kind for younger babies if that's what you're talking about.
They had the infant highchairs (with the molded seats shaped like an infant seat, reclining) at both Crystal Palace and Chef Mickey's on our last trip in January. DGrD was 5 1/2 mos old - everywhere else allowed us to bring our stroller to the table, but we were there off season and it wasn't terribly crowded.
We took our DS to WDW when he was 8 months old. I believe all the restaurants we went to had the wooden chairs and they worked fine for him. Good luck!