Congratulations on your successful frozen mountainhome!
To your question about ore: I'm no expert on geology (or DF geology for that matter), but I would say there is definitely a chance you'll find some new layers that could have ore down at the very bottom. Your best bet will be to breach the third cavern layer and get a peek at the magma sea, and that should expose it if there is any. Digging exploratory tunnels down to the magma sea is pretty easy, a lot of people do it in their first year.
Other alternatives. Galena certainly beats nothing. However I would look to goblinite for additional iron, bronze, copper, and silver. I've used this as my main copper/iron source before and it actually works pretty well with some clever stockpile management. You can make a weapons/armor stockpile that only accepts no-quality, non-steel weapons/armor, and when gobbos are dead, mass dump, then mass melt designation, which will overwrite the dump designation, then unforbid items from the stocks menu. Its fuel intensive if you don't have magma industries setup, but not prohibitively so.
Other notes: on a freezing biome with no soil, getting a quick tree farm up is a bit harder since you'll be required to dig out stone layers and flood them, but with no trees, no metal, and apparently not yet any magma, I think a tree farm is your only option if you don't have one. Caravans are pretty good about bringing logs, but don't bring enough to support a large metal industry, much less one that has to melt down items.
With minecarts and improved stockpiles, getting goblinite down to the magma, or getting the magma up to the surface is a bit easier. So a melting-based metal industry is more reasonable to operate than ever before.
With your fort being metal-challenged, I assume you've come up with some cool ways to take down masses of gobbos. One trap design I've always wanted to try on a all-freezing map would be a variant of the degrinchinator (if you haven't heard of it look it up).
EDIT: If you have cassiterite then you can convert your goblinite copper into bronze pretty easily.