It's possible you could experience some snow Tuesday night. Fox16 Meteorologist Greg Dee posted the following update on his Facebook page
The models are starting to come into more agreement about Tuesday's storm.
First, it all starts as rain on Tuesday. Everyone will be too warm for frozen precip. It's Tuesday night, as the low pressure moves to our east, that cold air moves in changing some of the rain to snow. The top row of maps shows where the precip is (snow & rain are both green with darker colors indicating heavier stuff) on Tuesday night. The snow is generally to the left of the dark dashed blue line. The bottom row of maps shows where each model thinks snow will fall Tuesday night.
As you can see, they're in pretty good agreement. All three models have snow generally falling west and northwest of Little Rock. Right now, this doesn't look to be a strong storm. So, accumulations would be rather light. They accumulations will also be very spotty with the snow sticking best the farther north you go and in more isolated areas farther south where temps may never get cold enough.
That being said, it's impossible to predict where exactly road conditions will be good or bad other than the farther north of I-40 you get the more likely icy spots will be. The overnight timing however will hopefully mean fewer people will be traveling in it. Anything that accumulates will quickly begin melting on Wednesday.
That's as detailed as I can get right now. The bottom set of maps is as precise as it gets so use those to "eye" whether your town falls in the snow or not. Little Rock looks to be out of this one.