(B) all one has to do with cattle is to leave them alone to feed themselves, to corral them, and
(C) all one has to do with cattle is leave them alone while they feed themselves and then corral them and

The main issue with B is not '...while they feed...", it is the use of '...to corral them, and to...'
".... all one has to do with cattle is to leave them alone to feed themselves, to corral them, and to drive them (now it appears that the cattle would do all these things and not the owner)..."
whereas in C, the sentence has a better flow stating that the cattle needs to be left alone only while they feed themselves.

Does that help..?