Fiona - for some reason/additive the winter salt they use is extremely tenacious
rheostatisticsfan - I still think I'd take them to a cleaners, but point out the salt and ask how they get it out. If you go to pick them up and still see salt, they should reclean them (although you may have to point it out to them again).
I've always somehow gotten salt out of fabrics. Usually a lot of water does most of it and washing does the rest. If yours can stand some water, try it before cleaning?
I haven't always been so successful with leathers/suedes. . . that's why all my lovely boots must take a hiatus until we get enough melting to dry out parking lots a bit - grrrr!