A province with a river running through it has the "fresh water" terrain tag. I think this means that the province is susceptible to flooding. Some spells may be able to take advantage of this fact.
There may be some other effects related to income and such, but I really don't know what they might be.
Numbness is a decent debuff spell for the early game. The Ice Pebble Staff at con-2 is a handy item for melee commanders who would otherwise sit around doing nothing.