What part of speech is 到 (to) when used in 两只饿到眼绿的老鼠正在房梁上打架? I was having trouble with the sentence


  两只饿到眼绿的老鼠正在房梁上打架


because I could not understand the usage of 到 here. After I spent some time thinking I figure the meaning is that the rats were hungry to the extent that their eyes turned green (a metaphor of some sort?) but if that is indeed the case, what would you call this type of word? In English I believe the word "to" used in this way is called a preposition but I haven't seen anything online about the usage of prepositions in Chinese.
You are essentially correct. Here, 到 is a preposition that, depending on context, can represent "to," "(up) until," or "up to." 

e.g. 到目前为止 : up until this moment

工作到天亮了 : work until the sky becomes light

从周一到周四 : From Monday to Thursday

In your particular example, there seems to be an implied “的程度" at the end of the descriptor which is omitted, i.e. one can write 两只饿到眼绿的程度的老鼠正在房染上打架, and in order to prevent a sentence from being clunky, this has been omitted since it's clear from context what is being said here.