The maximum number of USB devices on a bus is 127. From that number, you must substract the root-hub and all the other hubs that you need. Note that some hubs use more than one USB devices.
Also, some USB disks have an extra USB device in them. So, some disks count for 2 USB devices. So, to be sure, on the USB spec, you're limited to around 50 disks.
Another limit is the memory. If you have more disks, you have less cache per disk. In a system with 32 GB memory, that is not so much an issue. But for a Pi zero, that will be a limiting factor.
Also, USB performance becomes a bottleneck. There is not a hard limit here, but in vmstat you will see the wait-io rise if more disks are connected (and used).
Final judgement: you can connect 32 USB disks (I personally did 22 usb disks on a normal Pi 2), but don't expect any performance. At all.
---- Some additional research -----
http://www.yoctopuce.com/EN/article/how-many-usb-devices-can-you-connect states:
The Raspberry Pi 2 appears to work with 10 devices sending messages at
100Hz: this eats up about 12% of its CPU time. Over 10 devices, the
handling of High-Speed devices seems to slow down exponentially, and
it is even impossible to get 17 devices to work simultaneously, even
when they send almost no data.
This is different from my own experience; I was able to connect 22 drives, as long as I used only one drive at a time, and these are sensor/actuators (not drives). But it supports more or less the idea that 32 USB disks to a zero is not a good idea.