Geometry is very different I think… Cyclocross frames are deliberately designed for off / on road use so you can get your head up (more sit up & beg MTB stylee) as opposed to a racer which you are dropped into a streched crouch. The BB is higher A CX frame will have more mud clearance too and longer reach brakes.
I would suspect that CX frames are designed to flex wheras a road frame might not be so forgiving.
I would be wary of the carbon road forks off road as they may not be designed for the sudden shock loading you get say if you hit pot holes etc. They will be engineered to withstand a constant loading.
If its for the odd foray onto a dirt path or in snow then the CX tyres will be fine but if you are looking for a dedicated comp beast then there may be issues.
That said CX started as a form of winter training using road bikes with knobbly tyres.. so you may have no issues.