The amount of water in snow depends greatly on how "wet" the snow is. My guesstimate is that every 10" of Midwest snow will melt down into 2 inches of water. 2/3rds of Minnesota precipitation happens in the summer (
interweb) so I'm guessing you'd be looking at the equivalent of 8" of snowmelt water.
If you're watering a garden bed, the amount of water you need per square foot depends on how you're watering it and the condition of the soil. Conventional gardeners like to get an inch of rain (or irrigation) per week on the plants. From what I hear, greenhouses in the winter use much less water. So if you could collect snow and melt it for the greenhouse, it could be a good way to get water throughout the winter. Storing it up all winter for summer use would be much more challenging.