There is potential for a blizzard to unfold in the Plains between October 4th and October 6th.
High resolution model guidance supports strengthening of a powerful storm system as it shifts north and east through the Plains. Lower level wind speed is shown as high as 69.1 knots on this map, with the strongest winds bombarding northwest Minnesota and the Dakotas. Sea level pressure contours in South Dakota drop down as low as 992.0 millibars, per the graphic above. With American model guidance showing this scenario consistently over the past 48 hours, it appears a Plains blizzard is certainly a possibility.
Precipitation type and 3 hour precipitation amounts shown above project the development of a sub-freezing air mass across the western half of South Dakota, leading to very intense snowfall amounts and rates. High resolution guidance indicates there is potential for 10'' of snow in 3 hours (just over 3'' of snow per hour, on average), but considering this hi-res model guidance is notorious for over-estimating snowfall, one should use this map and the one below with caution.
The high resolution NAM model shows incredible amounts of snow across western South Dakota and southern North Dakota. Again, this very well could (and most likely is) be exaggerated, considering the past history of NAM model forecasts. Regardless of its exaggeration bias, the other American model (the GFS) agrees with the projection of significant snowfall, but it has totals in the range of 12-18'' maximum. Model guidances will most likely remain unresolved until the event actually happens, but I project very isolated pockets of 20'' snow totals in western South Dakota, with generalized 12-16'' across western South Dakota.