Current freshman, how much does wealth matter?

Unfortunately it matters but not in the sense that you can "flex" your way in. It matters a lot in terms of your relatability/background for the top/upper frats. For example, Sig Phi is almost (note almost not all) ex boarding school kids. Most of these guys went to schools like Choate, Andover, Deerfield and the super wealthy NYC privates like Horace Mann, Dalton. The other top frats, Sig Chi/DU also have a significant chunk of kids having gone to these top privates. Likewise AD is known for having a lot of wealthy international and nyc area kids. Ultimately to get into these top frats without prior connects, you would need to relate and fit in with these kids which unfortunately would be hard if you can't talk about where you summer or some cool traditions at your elite private school.

Ultimately this is Cornell. Every frat has a fair bit of wealth. It is just that it is a very high identity thing amongst those at the top.