Where to find reliable snowfall rate data?
Unfortunately, what you want may not be actually available. It is standard to make measurements of snow every 24 hours. This is because it is well known that frequent observations of snowfall will exceed the total accumulated snowfall.
The total accumulation of snow is not equal to the sum of the accumulated rate of the integral. That is, $$\Delta S \ne\int_{t_0}^{t_1}Rdt$$ where $\Delta S$ is the change in snow depth and $R$ is the snowfall rate. This is because compaction and melting both occur, changing snow depth.
That being said, you can make an approximation using daily snowfall depth observations. In the U.S., there are two systems that spring to mind. The first is the U.S. Cooperative Observation Program, which uses the standard in-situ observations of snow depth. The second is the NOHRSC, which has an analysis product (use this link for archived numerical data or this link for a graphical product).