TLDR Next chance of snow for northern UT is Sat into Sun with sunny skies until then.
High pressure and sunny conditions will be the norm for the northern Utah mountains through Friday. A weak system over Arizona will bring some clouds for southern Utah on Thursday.
As Alex mentioned, our next storm is slated for Saturday. Right now, it looks like it will produce a decent amount of snow, with valley rain/mountain snow starting around sunrise Saturday morning and snow levels 6000-7000 feet. The heaviest precipitation appears overnight Saturday to Sunday with the storm departing on Sunday. Monday appears to be an in-between day with more precipitation on Tuesday.