Got a ticket overnight, my windshield was covered in snow. Had a handicap permit. Is there a good chance I can take it to court and dispute it or should I pay and get over it?

It depends on what the ticket was for. Having a accessible parking permit in most jurisdictions simply allows you to use the designated spaces. Not park wherever and whenever you want.

This will depend on what exactly the ticket was for and what the bylaws in your city say about where you can park with a disabled parking pass. Some cities have exemptions for disabled parking pass holders to park in no parking zones or to exceed the maximum on street parking time limits and some don't.