carbocation = carbon cation
so nitrogen is just a cation
I am thinking that because nitrogen is a cation, it takes even more electron density from hydrogen, making hydrogen bonding between the hydrogen and the oxygen of water even stronger
but then you do not have the lone pair on nitrogen meaning you have less partial negative charge at nitrogen which might make hydrogen bonds to the nitrogen atom less strong
I don't know if these two things cancel out or make the molecule more or less soluble, but this is an interesting question