That is a huge problem, and it doesn't have any nice solutions. Dumping it in a lake should be banned of course, but keeping it in gigantic on-ground piles of dirty snow is only slightly better as it will quickly ruin a huge part of parkland somewhere in the central city (can't drive it very far). Making a few large dumping grounds with groundwater protection would be great, but nimby+cost likely makes it difficult.

judging by this years' winter weather, global warming might solve this.