Seeing as Water types with Ice Beam seems to be the main concern, I decided that I would do some research on what types can resist both.
Every typing that has a resistance to both Ice and Water
This really needed to be pointed out that we can't get a Pokemon that resists both Water and Ice without having the Water type involved. So you're going to need to make a decision if you want to mainly resist Water, Ice, or also have an Electric immunity for Thunder. All the typings that resist either Water or Ice and have an Electric immunity are as follows:
Water and Ice are both SE against Ground, which means it will never resist either even with the dual typing, which you probably already knew. We're going to have to be offensively minded when choosing the types because unless you want a Water type on a Sun team, we should probably focus on the offensive qualities a type can have against water types and maybe have a resistance to either Water or Ice, but you're still prone to getting a Thunder to the face unless you're Grass, Dragon, Electric, or Ground typed also. Ground and Dragon are assumed out of the question, so unless you'd like to give up resistance to Water and/or Ice for an immunity to Thunder, Ground shouldn't be used; and Dragon is one of the "Big 4" types that we're trying to stop in the first place. I didn't take the time to look for a dual STAB typing we can take advantage of, I'll leave that to someone else.
Contact me if you need monotype help, I'll be more than happy to oblige.