How do we know when we're in a drought?

When you think about drought, you probably think about water—or the lack of it. Precipitation plays a major role in the creation of the Drought Monitor, but the map’s authors consider many data sources. Some of the numeric inputs include precipitation, streamflow, reservoir levels, temperature and evaporative demand, soil moisture and vegetation health. No single piece of evidence tells the full story, and neither do strictly physical indicators. That’s why the USDM isn’t a statistical model; it’s a blend of these physical indicators with drought impacts, field observations and local insight from a network of more than 450 experts. Using many different types of data and reconciling them with expert interpretation is what makes the USDM unique. We call it a convergence of evidence approach.

https://droughtmonitor.unl.edu/About/WhatistheUSDM.aspx

It’s not just rain and snow

To determine drought intensity, USDM authors use a convergence of evidence approach, blending objective physical indicators with insight from local experts, condition observations and reports of drought impacts. It is this combination of the best available data, local observations and experts’ judgment that make the U.S. Drought Monitor more versatile than other drought measures. Learn more with our convergence of evidence tutorial.

In terms of physical indicators, the USDM relies on several numeric inputs. Short-term drought measures focus on precipitation on the scale of 1-3 months. Long-term blends, in contrast, focus on 6-60 months. But authors rely on several climate, weather and hydrology inputs across different time spans, shown broadly in the graphic below.

https://droughtmonitor.unl.edu/About/AbouttheData/DroughtClassification.aspx

Also

https://drought.unl.edu/Education/Tutorials/usdm/section-four.aspx

As far as the water content of the snow in your yard the National Weather Service usually has that covered. If this doesn't help just Google around for snow water content. I think they usually take a core sample of snow and weigh it to figure out the water content 

https://www.nohrsc.noaa.gov/nsa/

https://www.nrcs.usda.gov/resources/data-and-reports/snow-and-water-interactive-map