> he seems not to be irritated when we have him on the medicine from the vet.
What do they give that is working - tablets, Fuciderm, steroids? Might give us an indication of the precise problem...
Once things like worms, fleas, mites, anal glands etc have been checked I'd be looking at some sort of allergy. Your breed can be susceptible and having an itchy dog myself I know how distressing it can be for both dog and owner. If the problem has only started since the snow then I'd wonder about external irritants like pollen as a food allergy is likely to have shown up before now. However the area of itching doesn't sound like a pollen allergy as these are most likely on the belly, flanks and legs.
Allergies are notoriously difficult to diagnose and the vet will eliminate all other possible causes first, and may well just adopt a watch and wait policy with the usual medications such as those mentioned above. Has your dog ever shown signs like this before? Also, is he insured?