This is actually quite complex, and the short answer is that skinning a metal structure in carbon is not going to result in any significant gains in rigidity.
For one, your subframe has been designed by an engineer to be constructed from steel, which means that it's geometry has been designed with that material in mind. If it were designed to be constructed from aluminium, to achieve the same strength and stiffness it would require a different geometry - as it would if it were constructed from carbon. Rigidity is a function of material and geometry.
Carbon fibre is famously stiffer than steel, but many people forget that it is only significantly stiffer than steel in relation to it's density (weight). If you looked at the Young's Modulus (the measure of a materials rigidity), steel has a modulus of around 215Gpa, while carbon fibre has a modulus of around 228Gpa. If weight is of no concern, then steel is almost as stiff a material as carbon fibre for a given geometry. Where carbon fibre wins out is it's density; it is 5 times lighter than steel. Steel weighs
@8g per cm3, while carbon fibre weighs 1.6g per cm3.
To figure out what that means for you is tricky, but say your subframe was a flat piece of steel that was 10mm thick. If you wanted to make a replacement for that 10mm thick steel out of carbon fibre, then to achieve the same stiffness you would need a 9.4mm thick sheet of carbon (it would in fact have to be thicker, because you would need 9.4mm of just carbon NOT including the resin). The carbon sheet would obviously be much lighter.
Unfortunately it is even more complicated than that, because you don't have a flat bar of steel for a subframe, you have a geometric shape designed to resist stresses in certain directions. Now you are also getting into the comparison of isotropic (equal strength in all directions) materials like metal, to anisotropic materials like fibre-reinforced polymers which only have strength in the direction of the fibres. Which means that to work out how to make your subframe stiffer, you need to know what direction your stress is coming from, ie. is it tensile, compression, torsion, shear, etc? To increase resistance to those stresses with composites, you need to ensure your fibres are aligned with the direction of that stress, and then work out if the geometry is aiding you with carrying those loads. That could mean that in some directions where you have very little geometry, you may need to add 100 layers, and in others where the geometry is making the shape very stiff you might not need any layers.
It is for that reason that geometry is the answer to increasing the rigidity of components like this, and exactly why that Chromoly subframe has been designed like it has been. It is taking advantage of the high tensile strength and high rigidity of steel, while keeping the weight down by using a tube design with optimised geometry. You would see significantly greater improvements in rigidity by triangulating your steel subframe using tube steel, compared to skinning it with carbon. We haven't even begun to get into the complications of the structural integrity of a mechanical bond between the carbon and the steel, or the massive differences in elongation to break that would likely see the carbon fibre reach it's breaking point long before the steel even begins to feel stressed, unless the carbon was so thick that it exceeded the strength of the steel - at which point the steel becomes redundant and is only acting as an extremely heavy 'bulker' to the carbon.