who do you want to go walking with?whom do you want to go wa

恩,都对的
who作代词时,既可以用作主语,又可以用作宾语

都对。
who是主格，作主语；
whom是宾格，作宾语。口语中常用who代替whom。
原句who或whom是介词with的宾语。

If you want to speak English then you can say either of the above ones. And you can ignore what role every part plays in a sentence which can make you speak beautiful and natural English.
If you want to do a research into English language, save it to the graduate school.