I imagine the MVMCP is rain or shine, but it doesn't sound very fun to be there 7pm-12am, watching the additional parades and shows in the rain.
I'm not quite sure of the exact Disney policy on rain during the MVMCP, but I was listening to a DIS podcast from last year where they were talking about a Tuesday in November last year where Disney canceled the party and offered tickets for other dates and refunds. So it is not necessarily rain or shine.