2. lets take a step back and clarify military terms
in wars there are strategic moves and there are tactical moves, you seem to be confusing the 2
STRATEGIC is big picture, TACTICAL is small picture
it is correct that the STRATEGIC purpose of the army was to defend Winterfell, but Ramsey had made a TACTICAL decision that he was going to defend in the field, he could have easily made a different TACTICAL decision to defend winterfell from the inside ala Blackfish
at the STRATEGIC level, once he defeated the starks, he would be unchallenged, any anger over minor tactical decision made in the battle would not compare to the complete STRATEGIC advantage HE GAINED, the starks becuase of heir name and theoritical ability to call up banners were the only STRATEGIC threat to ramsey, no other houses would give 2 fuks about the fact that the umbers and karstarcks were used as fodder and the umbers and the karstacks would have no TACTICAL advantage since their men were dead
so his plan made sense
ramsey was using the umbars and karstarks as fodder, aftert the battle was over they would not be in a position challenge him
4. that wasnt stupid and they werent his men, once the starks were defeated ramsey would have overwhelming STRATEGIC power over the north, if he had won, which he was just about to, the umbers and karstacks would not have been in either A TACTICAL (they had few men) or STRATEGIC (no house would rally to them) position to challenge him
it was good plan, littlefinger and sansa ruined it