Why amine salts are soluble in water?
Amine salts are:


charged
polar
hydrogen-bonding (unless they're quaternary)


There some cross-over between those categories, but all will increase solubility in water, a polar solvent, and decrease solubility in a nonpolar solvent, like ether. 

That said, if you put very long oily carbon chains on an amine salt, you will decrease the solubility in water, and increase the solubility in nonpolar organic solvents.