TL; DR: A high pressure is centered over Utah right now, keeping the atmosphere dry through tomorrow morning when a storm arrives Tuesday and another on Wednesday.
Short term: A trough currently over the Pacific Northwest will move inland over the next couple days. As it does, Pacific moisture and lifting associated with the shortwave will produce light to moderate snow, with the heaviest snow over the far northern Utah mountains. Some light snow will make it into central Utah, but accumulations here will be minimal. A second wave arrives on Wednesday. This storm should be a bit more widespread and may produce more precipitation than the first because it will move slower and contain deeper moisture. Storm total accumulations for both waves will be about 10-20 inches with the greatest totals expected over the northern Wasatch.
Long term: Snow showers will linger through Thursday before building heights and dry air from an approaching high pressure clear things up. Friday will be dry as well before another system arrives on Saturday. This storm looks a bit deeper so the southern Utah mountains may get some snow out of it, but we’ll need to see if the models continue to show this in future runs.