Is there any chance that one can use snap to install packages in Cygwin?
Very unlikely to happen. Snap requires kernel support for features to isolate and confine applications. Much of the functionality of the system is predicated upon having these features available. Even the Windows Subsystem for Linux, which recreates a lot of the linux kernel, is incompatible because it doesn’t reimplement enough yet.
With WSL existing I think very little effort is likely to be directed towards cygwin going forward, favouring instead the binary-compatible Microsoft implementation. That means you’re unlikely to get a working snapd in cygwin, and marginally more likely to get it in WSL.
Well, Unfortunately the Windows 10 we got in our university doesn’t allow WSL 
I’m stuck with CygWin.