Gee, I thought you were going to ask about doing away with or combining the Fresh & Salt Forums.
Shelly, I wouldn't personally put a goldfish (non-tropical) with a Betta (tropical) in an unheated tank. While the goldfish can take a wide temperature extreme, a Betta should be in the 70-80 degree range. It is analogous to the CP plant cube combinations that Lowes does, by putting a VFT with a Darlingtonia with either a D. adelae or a P. primuliflora. they have differing requirements.
Can it be done? Yes, but it isn't the best combination. Do you have the typical tank set up with filter, pump, light, etc...?
Goldfish are also notoriously dirty and cloud up a tank in no time flat. Bettas, ironically, are what they call - anabantids. They can breathe atmospheric air. They naturally hail from stagnant rice paddies in SE Asia and have adapted to poor water quality.
Another thing to strongly consider is whether you are using a tank with an established filter medum. If so, the metabolic waste that they produce should be handled well enough. If you are emplacing a brand new filter in the tank, it is a set up for disaster because it needs to go through the nitrogen cycle (Ammonia->Nitrite->Nitrate). Water changes alone won't solve the situation. Once through the nitrogen cycle, then it will be safe to introduce other fish.
What would be the temperature for your area during winter? If it gets below 70, you run the risk of having ich killing the Betta and other fish - but not the goldfish. I know Washington State is more maritime in climate, but it is also a big State and you may not be on the Coast.