You might just buy a new hub or entire new wheel and be done with this.
Lacking the perfect replacement parts, just make do with what inexpensive stuff you can find. You might have to add spacers to get back to the OLD. Your seal might have to be a piece of thick rubber you cut and push in there. Used to be quite common for bearings to not be as well protected on BB's and axles. We just put excess grease on them and cleaned them more often.
I guess the big question is if this bike is worth spending the little bit of money an entire new wheel costs. Or just getting some cones that work even though not original spec. so you can ride this bike before another winter comes.