I cannot find a Yaakov Horowitz who dies in Vienna in 1631. I think he is being mistaken for R' Itzhak Halevi Ish Horowitz
I think the son Asher Zelig is mistaken for Asher Zelig Horowitz
I think the son Meshullam Zalman d. 1622 Krakow, supposedly the author of Darchei Moshe, is mistaken for Shmuel haLevi Horowitz