Forecasters are now predicting 1 to 2 inches of snow for Long Island, starting early Monday after midnight.
"If something drastically changes, we could get more," said Lauren Nash, a National Weather Service meteorologist in Upton.
Earlier, forecasters had said there was at least a 30 percent chance of up to 6 inches of snow, potentially impacting Monday's morning commute. Nash said Saturday the storm is staying farther south than originally predicted.
The snow is expected to continue into the early afternoon Monday, Nash said.
Temperatures will cool down Sunday, with highs in the mid-30s. The lows will be about 20, Nash said.