To "vanquish them horse and foot" means that she sent all comers away, be they on horses or walking. Here she is not being compared to anything per se, but her actions help the townspeople excuse their behavior of allowing her to descend into such an abysmal state.
" Vanquish" is a potent in this story that looks back to the time of the civil war for its context. To "vanquish" means to overcome, to conquer, and "vanquish horse and foot" resonates with civil war battles that the south ultimately lost. For a woman to vanquish men shows an upset of traditional roles, and indeed Emily, even though she is a traditional, southern lady--in fact, because she is a traditional southern lady-- has power over the town in such a way that they are afraid of her, and it is this distance that enables (or causes) her to deteriorate in the way she does in murdering (vanquishing) Homer and then preserving his body.
To vanquish horse and foot is to defeat completely. Before the advent of modren warfare, before machine guns and airplanes and mustard gas, warriors were either foot (infantry) or horse (cavalry). When Emily Grierson rebuffs the delegation sent by the city council by simply stating that shes has not taxes in Jefferson and urging them to "See Colonel Sartoris" she confounds them - Sartoris has been dead ten years. She then dismisses them and has Tobe show them out. She defeats them completely, metaphorically destroying their horse soldiers and their foot soldiers. She vanquishes them horse and foot.