Locally for South Carolina for Monday it will be sunny with high's ranging from the lower 50s closer to the coast to the mid to upper 40s in the upstate. Overnight it will be upper 30s near the coast and low 30s in the upstate. For the high on Tuesday the area near the coast will be highs of the upper 50s while the upstate will be around 50 degrees. Tuesday night is tricky as a cold wedge will begin to form. Depending how it sets up will really depend how cold it will get in places.
About the low pressure forecast to move across the United States. I have included a model run from https://www.tropicaltidbits.com/ which gives a ball park of what the snowfall could look like with the chances of some light accumulation of sleet/ice being just south of the snowfall. On Tuesday to Tuesday night it will likely drop 8-12 inches (with locally higher amounts) of snowfall in that pink area by mid to lower Missouri. Another pocket of heavy accumulation of 8-12 inches could develop near the Virginia coast; this snowfall would start Wednesday afternoon till the late morning of Thursday but this is of less confidence depending on how fast it starts to strengthen and the path it takes. Do note this isn't exactly what will happen because the low could still track higher or lower and other models show slightly different areas for heavier accumulations.

For us in South Carolina on Wednesday closer to the coast could see 0.5-1 inch of rain while the rest of the state is more uncertain in terms of rainfall depending on the track of the system. The winter weather will likely stay near the South Carolina/North Carolina border by Greenville and Charlotte on Wednesday. Wednesday night if the moisture can wrap around the back side of the low pressure, traces of wintery precip can't be ruled out as far south as Columbia.