Moisture is leaking through my basement walls, but the house is surrounded by concrete. Worth fixing?
I would get the ice away from the walls by a yard or so to try and minimize the incoming.

Drying out the damage is next - perhaps a dehumidifier...

Could you consider a drastic (and expensive probably) solution - by excavating down each outside wall and putting a treatment to seal the wall, also uses a plastic membrane (the one we had to use has "hats or thimbles" molded into it to make it 1/2" thick to allow the water to drain.

You could also consider adding a layer of insulation to the wall at the same time if appropriate...