The likes of me couldn't possibly draw bison, deer, and horses so as to tell them apart.

Literal

I-such-as [to-には] bison [and-と] deer [and-と] horse [and-と] [object-を] draw-distinguishing thing [such-as-など] absolutely can't-do.

A self-deprecating sentence about artistic skill. なんぞ is an archaic, humble variant of など meaning 'the likes of.' 到底~ない (absolutely cannot) emphasizes impossibility. 描き分ける (draw so as to distinguish) is a compound verb: 描く (draw) + 分ける (separate). The repeated と exhaustively lists the three animals.