Tractor FELs are not designed nor built to PUSH heavy loads. Something will buckle if your push regularly.
The forces applied to the FEL arms pushing a snow plow, do not differ from those exerted when driving with the bucket down, and pushing the bucket into a pile of dirt. And, they are most defiantly designed to do that.
Yes, there is a possibility of the plow hitting something and damaging the FEL. Just as there is a possibility or the bucket hitting something, and damaging the FEL, when using that. Or, a frame mounted plow hitting something and damaging everything. Any use of a tractor, carries with it, the possibility that some sort of damage can occur.
If the plow is sprung properly, it will actually trip and completely prevent damage, in a case where the FEL bucket could not do so. This is why I would rather have a plow, than a snow pusher.
With a proper set up, and reasonable care, it is most certainly possible to plow snow with a FEL mounted plow.